A day after House Republican infighting prevented them from electing a speaker, Senate Minority Leader Mitch McConnell is scheduled to appear with President Biden — a rare joint event that allies of the Senate GOP leader say shows his different vision for the party.

The White House-organized event, to tout a $1.6 billion bridge project that resulted from a bipartisan infrastructure law, is in McConnell’s home state of Kentucky. The longtime senator has become an increasingly vocal critic of former president Donald Trump and blamed him for perpetuating a sense of chaos in the GOP. Chaos was on full display in the House on Tuesday, which adjourned with no speaker and no clear path for what happens next. To McConnell allies, Wednesday’s event serves as a stark contrast to that disorder.

“It’s certainly a different business model,” said Sen. John Thune (R-S.D.), McConnell’s top deputy.

The differing approaches on both sides of the Capitol reflect a party that stands divided over its future direction some two months after a disappointing midterm election that kept Democrats in control of the Senate and handed Republicans a narrow and already unwieldy majority in the House. While Rep. Kevin McCarthy (R-Calif.) struggles to build support from hard-right members, McConnell is trying to promote bipartisanship and show that Republicans can govern. Meantime, Trump is waging another campaign for the White House that many in his party do not support, as others move closer to joining the race.

Wednesday’s event also highlights a new turn in the long and complicated history between Biden and McConnell, who served together in the Senate for decades and were occasional negotiating partners during the Obama administration — on opposing ends of the political spectrum but not always at odds. There is a clear political incentive for the president to appear with a Republican viewed with hostility by many in the Democratic Party.

Biden, who has said he intends to run for reelection, has sought to show voters that his ability to find common ground with political opponents yields results.

Mitch Landrieu, the White House infrastructure coordinator, said the White House planned the event to highlight bipartisanship, as well as cooperation between federal, state and local governments and between states. The White House invited Sens. Sherrod Brown (D-Ohio), J.D. Vance (R-Ohio) and Rand Paul (R-Ky.) along with McConnell to attend the event; only McConnell and Brown accepted, according to a White House official, who spoke on the condition of anonymity to speak freely about private conversations.

“If you think about the symbolism of tomorrow’s trip, it checks all of those boxes,” Landrieu said. “And it was done intentionally to demonstrate the president’s point of view of when you come together and you build big things, you can build a better America.”

Biden and McConnell will take the stage shortly after the House reconvenes to try to elect a speaker. After three rounds of voting Tuesday, McCarthy was unable to garner enough votes to secure the gavel, despite his entreaties to a group of right-wing holdouts.

To many, day one of the new Congress has called into question how effectively House Republicans will be able to pursue the achievements they promised during the midterms, including more oversight and investigations into the Biden administration.

Although the midterms delivered Republicans the House majority, the election left a bitter taste in the mouths of many hoping for much bigger gains. Last month, McConnell explicitly blamed Trump for the party’s underperformance, saying in an interview with NBC News that Trump gave the impression that “we were sort of nasty and tended toward chaos.” Despite being more supportive of Trump in the past, and sidestepping some of his most criticized moves, McConnell has taken the former president on more directly in recent weeks,

McConnell has also said he wants to find areas of compromise with Democrats as Washington enters an era of divided government and has explicitly called on House Republicans to not let the country default on its debt obligations as some have threatened to extract concessions from Democrats.

To Thune, Wednesday’s visit sends a message that Congress needs to function even in an era of divided government. “There’s a lot of things we disagree on, a lot of things we dig in and fight on, but we’re going to have to be trying to find those areas of common ground [so] we can put up some victories and hopefully get some solutions for the American people,” he said.

Biden, meanwhile, is betting that congressional compromise works in his party’s favor as well. As he sought the presidency, one of his main selling points was his track record of reaching across the aisle to Republicans to get results. Early in his presidency, he brushed off Republican attacks as senatorial bombast.

Biden has pointed to some of the past deals he was able to strike with McConnell, even as he’s left unsaid some of the key Democratic priorities McConnell helped block, including gun-control legislation in 2013 and a Supreme Court nomination in 2016.

According to people close to both men, there is a genuine respect and a civil relationship between the two despite their differences. They have looked for opportunities to work together.

“My message to [Biden] is let’s find some things between the 40-yard lines that we can agree on, and we did some of that this year: infrastructure, CHIPS, school safety, mental health,” McConnell said in November.

Biden and McConnell have a relationship that goes back decades, reflecting a time that rewarded dealmaking and honored a more clubby atmosphere. Even though they have often been at odds over policy, they have been careful not to wage personal attacks against each other to avoid damaging the relationship.

“We have significant disagreements, but we recognize the sincerity and the intellectual grounding of the other man’s position and the necessity of finding common ground,” Biden said during a February 2011 trip where he joined McConnell at the University of Louisville. “If you’re open-minded, it is impossible to not see the other man’s perspective.”

In the aftermath of the 2010 midterm elections, in which Democrats were roundly defeated, some had predicted that Washington would grind to a halt and Biden, then the vice president, remarked that he told President Barack Obama that he wanted to go sit down with McConnell.

The end result, Biden touted, was a tax deal that was “the only major compromise, only truly bipartisan event, that occurred in the first two years of our administration.”

The two men have tried to mend their relationship when the rhetoric grew heated, people close to the politicians say. During a voting rights speech last year, Biden appeared to compare Republicans opposing the legislation with Southern segregationists.

“How do you want to be remembered?” Biden asked. “Do you want to be on the side of Dr. King or George Wallace? Do you want to be on the side of John Lewis or Bull Connor? On the side of Abraham Lincoln or Jefferson Davis?”

McConnell railed against the speech, saying it was “beneath his office” and “unbecoming of a president of the United States.”

“How profoundly, profoundly unpresidential,” McConnell said on the Senate floor. “I’ve known, liked and personally respected Joe Biden for many years. I did not recognize the man from the podium yesterday.”

Biden, during a trip around that time to the Capitol, went into McConnell’s office in an attempt to meet with him directly. Biden wanted to explain to McConnell that he wasn’t likening him to the notorious racists and segregationists, but McConnell wasn’t there at the time, according to a person familiar with the situation who spoke on the condition of anonymity to describe private interactions.

While opportunities to work together have been limited — particularly as Biden pursued an aggressive health, climate and tax bill that passed last year that McConnell and Republicans were adamantly opposed to — the infrastructure bill they both supported has been touted by both Republicans and Democrats.

And both men see a benefit to connecting their names to the bridge work being done over the Ohio River.

The neighboring states of Ohio and Kentucky will get more than $1.63 billion from the infrastructure law to build a new bridge over the river and to make improvements to the existing Brent Spence Bridge.

The Brent Spence Bridge was built in the 1960s, when engineers said it should carry around 80,000 vehicles a day. Today, it carries twice that number, and the Federal Highway Administration has declared it functionally obsolete.

Politicians in both parties have been talking about reinforcing the bridge for decades. Obama once blasted McConnell for refusing to pass an economic plan that would repair a bridge that benefits his state. Trump vowed to replace the bridge when he was running for president in 2016 and said he’d pay for it by canceling “billions of dollars in global payment to the United Nations.”

For his part, Biden played down the significance of his appearance with McConnell on Monday, telling reporters as he returned to the White House from his Virgin Islands vacation that the Kentucky trip “has nothing to do about our relationship.”

“It’s a giant bridge, man,” he added. “It’s a lot of money. It’s important.”

Yasmeen Abutaleb and Theodoric Meyer contributed to this report.