COVINGTON, Ky. — President Biden delivered a celebration of bipartisan achievement alongside the Senate’s top Republican on Wednesday, even as House Republicans continued their chaotic debate over who can best wage partisan warfare against his administration.

Standing in front of the Ohio River, the president joined Senator Mitch McConnell of Kentucky, the Republican minority leader, and an improbable mix of political rivals to highlight new funding for the Brent Spence Bridge, which connects Covington to Cincinnati. The rare joint appearance is an effort by the White House to begin 2023 by focusing voter attention on instances of bipartisan agreement during Mr. Biden’s first two years in office.

“I wanted to start off the new year with this historic project here in Ohio, Kentucky, with a bipartisan group of officials, because I believe it sends an important message, an important message to the entire country,” Mr. Biden said in front of the bridge, which is a vivid symbol of the nation’s crumbling infrastructure.

“We can work together,” he said. “We can get things done. We can move the nation forward if we drop our egos a little bit and focus on what is needed in the country.”