(Bradley C. Bower/Bloomberg)

In two Statements of Administration Policy on Tuesday afternoon, the White House Office of Management and Budget said that it backs both H.R. 674, a House Republican bill to repeal the 3 percent withholding requirement on contractor payments, as well as H.R. 2576, the GOP’s proposal to pay for the withholding tax repeal by changing the rules by which some Social Security recipients qualify for health insurance subsidies.

Both measures are slated to come up for votes in the House on Thursday.

The withholding rule became law in 2006, but its implementation has been repeatedly postponed; most recently, President Obama proposed in his jobs package this fall that the regulation be delayed until 2014.

Bipartisan supporters of the withholding tax repeal argue that while the regulation is aimed at preventing tax evasion, it would unduly burden the majority of government contractors who are playing by the rules. Repeal supporters also contend that the cost of implementing the withholding rule would wind up exceeding the amount of new revenue brought in.

The prime area of disagreement between the parties is not whether to repeal the withholding rule but rather how to pay for the cost of repeal. Senate Democrats prefer paying for the repeal by eliminating corporate loopholes for corporate jet owners and similar measures aimed at higher earners, while House Republicans have put forth their competing proposal that would change insurance subsidy requirements for those receiving Social Security.

Last week, Senate Democrats blocked a Republican move to advance the repeal measure, citing their opposition to the Senate GOP’s pay-for, a proposal to rescind unused federal funds.

A spokesman for Senate Minority Leader Mitch McConnell said that the Kentucky Republican “is encouraged to see that the president will now support this provision of his own bill.”

“While we tried to pass it last week with a different bipartisan offset, Democrats blocked it,” McConnell deputy chief of staff Don Stewart said. “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.”

Michael Steel, a spokesman for House Speaker John A. Boehner (R-Ohio), said House Republicans welcomed the news of the White House’s support for the withholding tax repeal and urged the Senate to take up more than a dozen House-passed measures that Republicans say will create jobs.

“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,” Steel said in a statement. “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.”

The White House statements on Tuesday give a boost to the House Republican proposals, although it is unclear whether the Senate — which is on recess this week — might take them up if they pass the House as expected Thursday.

And not all House Democrats are on board with the proposal, as House Democratic Caucus Chairman John Larson (Conn.) noted Tuesday morning.

“I don’t think it’s as bipartisan as the Republicans would like to couch it by any stretch of the imagination,” Larson told reporters after House Democrats’ weekly caucus meeting. “There’s been a long-standing concern in the Democratic caucus about the pay-fors as they relate to Medicare and Medicaid and that is problematic. And, especially in the context of the committee that’s taking up a much larger and what should be a bold, balanced, and big initiative, that’s where the problems would stem from the Democratic side.”

The White House said in its statement on the repeal measure that the bill “would reduce a burden on government contractors who otherwise comply with their tax obligations, particularly small businesses. ... The effect of the repeal of the withholding requirement would be to avoid a decrease in cash flow to these contractors, which would allow them to retain these funds and use them to create jobs and pay suppliers,”

In its statement on the GOP’s pay-for proposal, the White House stated that “beginning in 2014, this income definition will be used to determine financial eligibility for Medicaid and the State Children’s Health Insurance Program, and for premium tax credits and cost-sharing reductions available through Affordable Insurance Exchanges. The Administration looks forward to working with the House to ensure the bill achieves the intended result.”