Come October, even though McConnell will campaign for Republicans in hopes of taking Reid's job as Majority Leader, the two can at least agree on one thing: Each wants the Washington Nationals to win the World Series.
In that regard, Reid and McConnell are like any other Washington baseball fans. Both are also unsure how the Nationals will do without Stephen Strasburg, the dominating 24-year-old whom the team shut down to protect his surgically-repaired right arm.
"They have a shot (at winning the World Series), but they are going to miss Strasburg significantly,'' says Reid, who has been Senate Majority Leader since 2007.
"The Nationals have a lot of good pitching, but we're all wondering if we are going to be as good without Strasburg,'' says McConnell, the Minority Leader.
The Nationals have reversed the dismal course of losing in D.C., and given that postseason baseball is returning for the first time since the Washington Senators lost the 1933 World Series, the city -- and the political establishment -- is buzzing with the Nationals at a time when Redskins football usually takes center stage.
"Football is a mistake and baseball is a habit,'' political columnist George Will says. "Washington is developing a good baseball habit. It can only help the civility (in Congress).''
Reid experiences the habit daily. He can't go anywhere without someone asking him about outfielder Bryce Harper, 19, a Las Vegas native who is among Reid's most-famous constituents. Even President Obama and Reid talk about Harper, who came up on April 28, played in the All-Star Game and is a candidate for the NL's Rookie of the Year award.
"How big is he? He's 6-foot-3 and weighs 220 pounds,'' Reid says. "He's very quiet and a super nice guy. And he comes from a really good family. I use him as a foil to the Republicans. I've said to people, 'The only person in Washington more powerful that Bryce Harper is Grover Norquist,'' referring to the president of Americans for Tax Reform, an organization that opposes tax increases.
Washington baseball used to be known for the slogan, "First in war, first in peace and last in the American League,'' but that's all changing. Until this season, Washington's biggest baseball hero in the last half century was outfielder Joe Hardy, a fictional character in the Broadway play Damn Yankees, which debuted in 1955.
Now, though, the Nationals have the best record in baseball and are on the verge of clinching the National League East with a team that has the league's best rotation, an air-tight defense and a lineup that can both manufacture runs and hit the ball out of the ballpark.
Washington's baseball team, alternately known as the Senators and Nationals, was a charter member of the American League in 1901. The team moved to Minnesota and became the Twins in 1961, the same year an expansion team replaced them in D.C. That version of the Senators left in 1972 to become the Texas Rangers. In 72 seasons of American League baseball, Washington's two teams won three pennants and just one World Series, in 1924.
The last contending team was in 1945, when the Senators lost the AL pennant to the Detroit Tigers by 1½ games. Since the Montreal Expos became the Nationals in 2005, the team is having its first winning season and erasing the memories of two 90-loss seasons and another two with triple digits.
Nationals Park, a mile from Capitol Hill, is a perfect mix of baseball and politics, fun and patriotic. From the upper deck, looking beyond leftfield, there's a picturesque view of the Capitol Dome that lights up as the sky turns to night. After the third inning, a group of military veterans attending the game are recognized on the video board and given a standing ovation. Then, in the middle of the fourth inning, there's a race of presidential mascots George Washington, Thomas Jefferson, Theodore Roosevelt and Abraham Lincoln.
Roosevelt, despite being the most athletic of the four in real life, has never won the race. In true Washington fashion, that brings debate. Sen. John McCain (R-Ariz.) said that it was unfair that Teddy had never won a race, and in a White House briefing, Obama spokesman Jay Carney agreed.
"This is an outrage,'' Carney says. "I agree with Sen. McCain. I'm comfortable saying my boss agrees with Sen. McCain.''
Obama, of course, is a White Sox fan, but he has told cheering crowds In northern Virginia, a key swing state in the presidential election, that he wants to see the Nationals play the Sox in the World Series. Sometimes, fans pay attention to politicians' sports allegiances, says analyst Jeff Greenfield.
"The best example is John Lindsay's 1969 reelection [as New York City mayor] when the New York Mets became champs,'' Greenfield says. "We in the Lindsay campaign hooked him at the hip to the team, even though he cared little about baseball. The New York Times picture of Lindsay being sprayed with champagne after was the pennant win was a clear political plus.''
This season, D.C.'s powerbrokers are hooking up with the Nationals. The team has had had five Supreme Court Justices -- John Roberts, Anthony Kennedy, Elena Kagan, Stephen Breyer and Sonia Sotomayor -- attend games, and so have Vice President Joe Biden, a Phillies fan, Attorney General Eric Holder, Defense Secretary Leo Panetta and several cabinet members, including Kathleen Sebelius (Health and Human Services), Hilda Solis (Labor) and Ray LaHood (Transportation). Ben Bernanke, the chairman of the Federal Reserve Board and a season-ticket holder, has been seen, in faded jeans, polo shirt and weathered Nationals cap, standing in line buying ice cream or visiting with Nationals players in the home dugout before the game.
"When you play in Los Angeles, you meet movie stars,'' Nationals outfielder Jayson Werth says. "When you're playing in Washington, you meet people that run the world. That's pretty cool. But you have to win. These people weren't around last year when we weren't winning.''
Werth tried to ask Bernanke questions about QE3, the latest round of economic stimulus, but Bernanke preferred balls and strikes, Werth says: "He wasn't talking about that economic stuff. So we talked about baseball, and it was a hoot.''
Military leaders like Martine Dempsey, the chairman of the Joint Chiefs of Staff, and his vice-chairman, Sandy Winnefeld, have also been in attendance. Winnefeld loves going to the games, for the baseball and for the thrill of seeing the wounded warriors get recognized. He puts on a red Nats cap as soon as he gets to the yard.
"It gets me out of the Pentagon, so that it always a great thing,'' Winnefeld says. "I appreciate the effort the Nats make in reaching out to our wounded warriors, to have them at each game, then the salute to our service members at each game. That is such a great thing to do, and watching the patriotic response from our wonderful Nats fans.''
Gen. David Petraeus, the director of the CIA and Winnefeld visited the clubhouse. They were excited to meet the players as the players were to meet them.
"You see hear about these guys in the news and then you see them in person,'' Strasburg says. "It's amazing. They look smaller than they do on TV.''
Strasburg posed for pictures and told Dempsey about his family's military background. Strasburg had two cousins who served and his two grandfathers, Roger Strasburg and Robert Swett, were in the Air Force during World War II. The grandfathers had the same initials -- RES -- so Strasburg showed Dempsey that he had those letters stitched in red into his black leather glove.
"I told him that my grandfathers shared a lot of stories with me about World War II and I understand the huge sacrifice that it requires,'' Strasburg says. "I admire those who serve. I called my mom to tell her that I had told them about our family, and she was freaking out. ''
Nationals pitcher Gio Gonzalez was freaking out as well when he met Petraeus and Winnefeld. Petraeus asked Gonzalez about pitching grips. Winnefeld, who has a 14-year-old son, asked Gonzalez what he was doing to be a better player when Gonzalez was 14.
"I just didn't want to say something stupid and be an idiot around people that powerful,'' Gonzalez said.
When Harper was promoted from the minor leagues in April, Reid called the family and said he'd do whatever he could to help their son. The senator made a recent trip to the Nationals clubhouse to see Harper and also stood on the field and watched batting practice. "It's hard to comprehend how good these guys are,'' Reid says. "They are gifted athletes.''
Harper pays little attention that he's part of the Washington establishment's conversation. "It's nice,'' he says. "I'm blessed to be in a city like this.''
Reid and McConnell might pound on each other, but there are no bigger baseball fans on the Hill. They say baseball gives them common ground. In his office, Reid has an autographed bat from Harper but he also has souvenir bats from Louisville Slugger, a gift from McConnell and his home state.
The senators talk baseball daily. Aides include baseball stories in the press clippings that land on their desks. They like that closer Drew Storen's stuff is becoming electric. Both wonder if the Nationals will keep first baseman Adam LoRoche next season -- there's a mutual $10 million option on his contract -- or work out a deal where prospect Tyler Moore gets more playing time.
Reid likes watching second baseman Steve Lombardozzi and McConnell says he loves low-scoring games, when the little things, such as a sacrifice fly, determines the outcome. They both get a kick out of watching the Nats' 70-year-old manager, Davey Johnson.
"Baseball is fun, and it gives us something to talk about, from both sides of the aisle,'' McConnell says. "Harry and I are a good example of that.''
Says Reid: "Mitch and I talk about baseball more than anything else. I love baseball because of the reasons people don't like it. It is mellow.''
As a kid growing up in Search Light, Nev., Reid's first team was the Cleveland Indians. He can recite the entire lineup of the world champion 1948 Indians. He also liked the 1960s Los Angeles Dodgers when Sandy Koufax and Don Drysdale were pitching for them. McConnell grew up in Puscumbia, Ala., and was raised in southern Louisville, and followed his dad's team, the Brooklyn Dodgers.
McConnell's home state of Kentucky is divided between Cincinnati Reds fans in the East and St. Louis Cardinals fans in the West. But the Nationals grew on McConnell from the moment they arrived in D.C. in 2005. He chuckles at how, in the early days, Nationals broadcasters had to put a positive spin on teams that were constantly losing.
But now the Nationals are easy to follow, "with all the players like Harper, Strasburg, Ryan Zimmerman, Jayson Werth, Adam LaRoche. You just become enthralled with them.''
In a town this divided perhaps it should come as no surprise that even the Nats can't inspire unanimity.
"The Nationals are a young team and definitely the most exciting sports team in Washington,'' says Sen. Jay Rockefeller (D-W. Va.). "But I'm an Atlanta Braves fan.''