Updated: 7:15 p.m.

The White House and House Republican leaders are on the same side on jobs, for once.

The White House backed the GOP leadership’s latest jobs bill today, which Republicans carved out of President Barack Obama’s own jobs package and paid for with a piece of his deficit reduction proposal.

White House Press Secretary Jay Carney said that the administration supports the House’s bill, which would repeal a 3 percent tax withholding requirement for government contractors that was enacted under George W. Bush’s administration.

“We support working with them to get that done, and we believe we can,” Carney said. “The current pay-for in the House version is something we can support.”

The White House had threatened to veto a similar measure that Senate Republicans offered last week, which would have been paid for with unspecified cuts in discretionary spending.

Don Stewart, spokesman for Senate Minority Leader Mitch McConnell (R-Ky.), warned against tying the repeal to items the GOP will not support.

“Sen. McConnell is encouraged to see that the President will now support this provision of his own bill,” Stewart wrote in an email. “While we tried to pass it last week with a different bipartisan offset, Democrats blocked it. Now, with the President’s support, the Senate should take it up next week, without adding poison pills, and send it to the President for his signature.”

Senate Democrats have yet to figure out their next move. “We are still working out a path forward,” a Democratic leadership aide said.

Carney tempered the show of bipartisanship with criticism for Republicans, saying they have yet to demonstrate that they will back a significant jobs package.

“What we still have not seen from the Republicans is a willingness to do the kinds of things that will substantially add to economic growth and job creation in the near term,” he said. 

Michael Steel, a spokesman for Speaker John Boehner (R-Ohio), pushed for more cooperation on the GOP’s agenda.

“We’ve said for weeks that there is common ground on jobs, but getting more done will require the President to work with us and actually engage in the legislative process,” he wrote in an email. “He can start by encouraging the Senate to act on this bill and the more than 15 jobs bills that have passed the House, many with bipartisan support.”

Earlier in the day, House Democratic Caucus Chairman John Larson said Republicans are trying to play “gotcha politics” by bringing to the bill to the floor, saying that the president “recommended it in the context of a bigger package,” not as a stand-alone bill.

“This is what the American people tire of,” the Connecticut lawmaker said. “People want to play gotcha politics instead of saying, ‘Look, we’ve got a big issue we’ve got to solve here.’”

However, the president himself advocated breaking his larger jobs bill into separate bills after the Senate blocked the package this month. Besides a Senate vote on a GOP-offered repeal of the withholding mandate, the Senate voted on a proposal to provide $35 billion to keep teachers and first responders from being laid off. Both items failed on procedural votes.

Daniel Newhauser contributed to this report.