What do you get when you pair a tea party champion with one of Congress’ most progressive lawmakers in the Senate? The people of Wisconsin are about to find out.

In perhaps one of the starkest examples of how bipolar the American electorate has become, the Badger State elected Sen. Ron Johnson (R) in 2010 over three-term Democrat Russ Feingold and Rep. Tammy Baldwin (D) ahead of longtime Republican stalwart Tommy Thompson on Tuesday.

And if statements already made this week are any indication, the coexistence between politicians like Johnson and Baldwin might be uneasy at best, especially as Republicans elected in the 2010 GOP wave adjust to life in Washington when Democrats are riding their own high.

“Hopefully, I can sit down and lay out for her my best understanding of the federal budget because they’re simply the facts,” Johnson told the Associated Press in an interview published earlier this week. “Hopefully she’ll agree with what the facts are and work toward common sense solutions.”

Johnson told the AP that he believed the Democrats’ performance in Wisconsin — President Barack Obama won by nearly 7 points and Baldwin 5.6 points — was based on a more uninformed electorate than the one that kept Republican Gov. Scott Walker in office earlier this summer after an unsuccessful recall attempt.

“I am concerned about people who don’t fully understand the very ugly math we are facing in this country,” Johnson said.

In an interview with Roll Call when asked about his previous comments, Johnson added that he was making “a very general comment about people, including members of Congress,” on budget issues.

“I’m concerned about people who don’t understand the fiscal situation … Very few people fully understand all of the information I’m providing,” Johnson said. “I’m concerned about people who don’t understand [the] true fiscal situation, and how vital economic growth is to [solving our fiscal problem].”

“People don’t understand that when they vote for people based on slogans,” Johnson “People don’t know … numbers.”

Baldwin has not directly responded to the suggestion that she, a seven-term member of the House, needs the budget explained to her, but told the AP that, “One aspect of all people who seek public service is that they care deeply about their state,” adding that, “There are some things we can find common ground.”

Baldwin also said that her state’s voters want to end the stalemate in Washington. “I know it’s a message that I take to heart, that I conveyed during the course of my campaign,” she said. “I think any elected official who’s aware of that message should take that to heart.”

When asked for comment about the existing relationship between Johnson and outgoing Sen. Herb Kohl, D-Wisc., Kohl’s office did not provide formal comment and instead pointed to a Nov. 2011 article about a dispute between the two senators over judicial nominees.

Johnson wanted to break with precedent and change the composition of the Federal Nominating Commission in the state, which had been used to fill every judicial and U.S. attorney vacancy since 1979.

“The Commission, whose structure is determined by a charter, has served our state well, through the tenure of Democratic and Republican senators and under both Republican and Democratic presidents,” Kohl said at the time. “So it’s been a great disappointment that Sen. Johnson has sought significant changes to the Commission.”

Despite the dispute with Kohl, Johnson told Roll Call he looks forward to working with Baldwin on projects important to Wisconsin, especially infrastructure, and highlighted a bridge project he worked on that also had the support of Kohl and Minnesota Democratic Sens. Amy Klobuchar and Al Franken.

Awkward tension between same-state, opposing party pairs, however, is neither new nor unique to Wisconsin.

Senate Majority Leader Harry Reid, D-Nev., for example, has been paired with a GOP junior senator for more than a decade. He brokers a sort of détente with his fellow Nevada senator, and treaded lightly around the sex scandal that ultimately led to Republican John Ensign’s resignation in 2011.

In his first press conference after this week’s election, he addressed his relationship with GOP victor Dean Heller, who had been appointed to replace Ensign and defeated Reid-backed Democratic Rep. Shelley Berkley.

“Dean Heller and I have been friends for 25 years,” Reid said, though the leader has been known to use the term “friend” liberally when talking to reporters. “I have affection for Dean Heller. I like him a lot. We’ll be able to work together. I worked with John Ensign, who I beat by 428 votes … and I think that you, everyone, has to acknowledge what good friends we are and how well we work together. So I have no problem with that.”

With Tuesday’s election, re-elected Democrats like Claire McCaskill of Missouri, Bill Nelson of Florida and Sherrod Brown of Ohio ensure that mixed-party intrastate representation is more common than it once was.

David Drucker contributed to this story