The House was headed for a cliffhanger vote Thursday on a revised debt plan from Republican Speaker John Boehner that could go a long way in determining if the government’s borrowing limit is raised in time to avoid a possible default next week.

Mr. Boehner scrambled Wednesday to stem defections by conservatives, telling fellow Republicans, “I need an army behind me.” But he could delay the vote if he concludes his plan won’t pass the House.

If it does pass, Senate Majority Leader Harry Reid (D., Nev.) prepared to put it to a vote in the Senate, hoping to defeat it. He then could try to push through his own debt plan, or make changes to Mr. Boehner’s plan to make it more palatable to Democrats.

Meanwhile, senior Democratic aides said Mr. Reid and Senate Minority Leader Mitch McConnell (R., Ky.) are exploring ways to bridge the gaps between the House and Senate bills and craft an alternative that can pass both chambers by Aug. 2. A spokesman for Mr. McConnell said the Senate Republican leader isn’t working on any bill other than one by Mr. Boehner.

Even as both sides press ahead with their plans, back-channel conversations between Messrs. Reid and McConnell focus on the biggest divide between the parties: whether to raise the debt ceiling in one phase or two, the Democratic aides said, reflecting a recognition that neither of the bills put forward by Mr. Boehner and Mr. Reid is likely to pass both chambers unchanged.

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