Faced with surging numbers of out-of-work Americans, many House Republicans are expected to break from leadership and vote to extend unemployment benefits as soon as Wednesday.

House Minority Leader John Boehner (R-Ohio) will vote against what could be a stand-alone bill on the issue, but a Republican aide said, “I expect members would vote for it.”

But the bill does face at least one possible glitch in the House. The plan violates the House’s pay-as-you-go, or pay-go, budgetary rules. Members of the Blue Dog Coalition, which advocates for strict adherence to those rules, are debating whether they should try to block the legislation.

“If we can muster the votes, they may have to pay for it,” said Rep. Jim Cooper (D-Tenn.), a member of the Blue Dog Coalition.

But other Blue Dogs say they are not inclined to take a stand on what many view as a technicality. Unlike the $52 billion “new GI bill,” which has provoked a confrontation with leadership, the unemployment extension is an existing program and expires after two years. Even Cooper called it “a closer question” than the GI bill.

“It’s very different,” said Rep. Allen Boyd (D-Fla.). “It does technically violate pay-go. It’s one shot, for 13 weeks. The GI bill is in perpetuity.”

Currently, people who are out of work can get unemployment checks for 26 weeks. The legislation would extend those benefits for an additional 13 weeks, and an extra 13 weeks after that in states where unemployment exceeds 6 percent.

House leaders had decided last week to drop the extension from the emergency war-spending bill, despite protests from Senate leaders. But when the Labor Department reported that the unemployment rate had jumped from 5 percent to 5.5 percent, the largest monthly increase in 20 years, lawmakers scrambled to change plans.

There is some debate in Democratic ranks about whether to continue with a stand-alone bill, include it in the House supplemental, or merge it back into the Senate supplemental. Without war funding attached, it is more susceptible to a veto by President Bush.

“It’s very possible it will be in both,” said a Democratic aide. “One does not preclude the other.”

A stand-alone vote also allows Democrats to put Republicans on the spot in an election year amid deepening fears about the economy among voters.

“They’re going to have to explain to their constituents who are out of work because of the Bush economic policies why they won’t help,” said Rep. Chris Van Hollen (D-Md.), chairman of the Democratic Congressional Campaign Committee.

But Republicans contend that GOP incumbents in swing districts will benefit from voting against their leaders and for the extension.

“Only the Democrats would give Republican members in battleground districts the opportunity to vote for unemployment insurance and call it a victory,” said a GOP leadership aide. “That’s nonsense, because those members have voted for something that will help them in the fall — even if leadership opposes it.”

Keeping it in the supplemental, coupled with war funding, could make it harder for Bush to veto as the Pentagon ramps up warnings that it will soon run out of money and pressures for swift passage.

The AFL-CIO, a key supporter of the extension, wants it kept in the supplemental.

“Right now it looks like the supplemental is the best way,” said Bill Samuels, the union’s legislative director.

President Bush threatened to veto the emergency war-spending bill if the unemployment extension was included.

The administration has argued that Congress should wait to see the impact of the economic stimulus passed earlier this year. Republicans have also argued that the unemployment rate is lower than the 5.7 percent rate when Bush extended unemployment benefits in 2002. Republicans have also advocated limiting the extension to states that have unemployment rates above 6 percent.

While the unemployment debate plays out, House leaders are negotiating with the White House and the Senate to find a bill that can pass both chambers and avoid a veto.

“It’s not on for this week, it’s not off for this week,” House Majority Leader Steny Hoyer (D-Md.) said.  “We want to pass a bill the president will sign.”

Jackie Kucinich contributed to this article.