Biden, McConnell greet Liz Cheney at joint address

Rep. Liz CheneyElizabeth (Liz) Lynn CheneyThe Hill's 12:30 Report - Presented by Goldman Sachs - Tokyo Olympics kick off with 2020-style opening ceremony The Hill's Morning Report - Pelosi considers adding GOP voices to Jan. 6 panel Democrats plow ahead with Jan. 6 probe, eyeing new GOP reinforcements MORE (R-Wyo.), garnering headlines this week amid a fresh round of GOP tensions, sparked a rare moment of bipartisanship on Wednesday night.

Cheney, the No. 3 House Republican, was seated along the House's center aisle and got a greeting from both President BidenJoe BidenBiden authorizes up to 0M for Afghan refugees Poll: 73 percent of Democratic voters would consider voting for Biden in the 2024 primary Biden flexes presidential muscle on campaign trail with Virginia's McAuliffe MORE and Senate GOP Leader Mitch McConnellAddison (Mitch) Mitchell McConnellHas Trump beaten the system? Yellen to Congress: Raise the debt ceiling or risk 'irreparable harm' The Hill's 12:30 Report - Presented by Goldman Sachs - Tokyo Olympics kick off with 2020-style opening ceremony MORE (R-Ky.) as they each, respectively, entered the chamber.

McConnell exchanged a lengthy handshake with Cheney, who he stood behind against attempts to oust her from her leadership position, by allies of former President TrumpDonald TrumpPoll: 73 percent of Democratic voters would consider voting for Biden in the 2024 primary Biden flexes presidential muscle on campaign trail with Virginia's McAuliffe Has Trump beaten the system? MORE. The two appeared to exchange words.

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Biden then subsequently gave her a fist bump on his way up to the House podium.

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The dual greeting comes even as the two men involved — McConnell and Biden — are at odds over much of the administration's agenda.

McConnell and Biden served in the Senate together and cut deals under the Obama administration. But McConnell disclosed earlier this year that they had barely spoken and he knocked Biden's first 100 days from the floor earlier Wednesday.

Cheney, meanwhile, is facing revived tensions within this House GOP caucus this week, including breaking with House Minority Leader Kevin McCarthyKevin McCarthyHas Trump beaten the system? Yellen to Congress: Raise the debt ceiling or risk 'irreparable harm' Freedom Caucus presses McCarthy to force vote to oust Pelosi MORE (R-Calif.).

Cheney told reporters at a House GOP retreat that she viewed McCarthy and McConnell — not Trump — as the leaders of the GOP and broke with McCarthy over the scope of a Jan. 6 commission.

She also floated, in an interview with the New York Post, that leading the effort to overturn the election—which many of her House GOP colleagues and a handful of Senate Republicans supported — is "disqualifying" for those thinking about running for the White House in 2024.

Trump lashed out at Cheney in a statement this week and McCarthy declined to say if Cheney was a "good fit" for the GOP's leadership team.