If House Republicans are able to approve a short-term extension of the debt ceiling, Senate Democrats likely would struggle to avoid taking it up, and it could force leaders to produce a budget when they ordinarily would have discouraged it.

The White House announced Tuesday that it would not oppose the pending short-term measure, even though the administration’s preference would be for a longer-term solution. Senate Majority Leader Harry Reid, D-Nev., largely deflected questions Tuesday when asked about the debt limit deal that the House is expected to vote on Wednesday. That bill is expected to include language that would tie Senate passage of a budget to senators’ ability to be paid. The chamber has not taken up a budget resolution in more than three years.

“I’m happy to extend the debt ceiling without entitlement cuts or dollar-for-dollar [cuts], so that’s a step in the right direction,” Reid said after his weekly caucus luncheon. But he told reporters that any further questions about the budget should be directed toward new Budget Chairwoman Patty Murray, D-Wash.

Within an hour of his comments, the Office of Management and Budget issued a statement declaring that President Barack Obama would not veto a short-term agreement. The House bill would prolong the nation’s borrowing capacity until May.

“The Administration supports a long-term increase in the debt limit that would increase certainty and economic stability,” the statement read. “Although H.R. 325 is a short-term measure and introduces unnecessary complications, needlessly perpetuating uncertainty in the Nation’s fiscal system, the Administration is encouraged that H.R. 325 lifts the immediate threat of default and indicates that congressional Republicans have backed off an insistence on holding the Nation’s economy hostage to extract drastic cuts in Medicare, education, and other programs that middle-class families depend on.”

Though a short-term deal is not a preferred method of dealing with the issue for most in Congress, Senate Republicans seemed open to taking up the bill as well if their House counterparts can send it their way.

Senate Minority Leader Mitch McConnell, R-Ky., would not say explicitly whether he would endorse the short-term plan, but the Senate GOP leadership team seemed to relish in the idea that House Republicans had returned to the budget message with this legislation.

“We look forward to seeing what Senate Democrats recommend,” McConnell said, when pressed on whether he would support a three-month deal.

McConnell also suggested Senate Democrats, if they were averse to anything but a clean debt ceiling increase, could come up with legislation of their own. With Obama essentially promising to sign the House bill, however, it’s unclear what kind of leeway Senate Democrats would have to act alone.

“Follow the regular order. The debt ceiling can originate in either house. The Senate Finance Committee could generate a debt ceiling proposal. They could do it clean if they wanted to,” McConnell said after the weekly caucus luncheons. “They could try to embrace some spending reduction. But I think what the House is saying above all else is they’re hoping to act, as soon as maybe tomorrow. And then it will be incumbent upon the Senate Democratic majority to come up with what is their idea about raising the debt ceiling.”

Some Democrats agreed with McConnell. Sen. Mary L. Landrieu, D-La., expressed doubts over whether the House proposal would pass muster with Senate Democrats. “We’ll pass an extension, but it’s not going to be on the terms of the House of Representatives,” she said.

Others said they would reserve judgement until after House passage. Majority Whip Richard J. Durbin of Illinois and several other Democrats such as Debbie Stabenow of Michigan and Thomas R. Carper of Delaware said they would need to study the House proposal before deciding to support it. Carper said that if the extension is passed by both chambers, lawmakers should “use the time to develop a bipartisan deficit deal.”

The House looks likely to approve the measure Wednesday — prospects that were likely aided by the Club for Growth’s decision to hold their fire on the measure.

Alan K. Ota contributed to this report.