The chairmen of the White House’s debt-reduction commission are making last-minute changes to their provocative early draft in an effort to broaden support before a crucial Wednesday vote, people familiar with the matter said.

The co-chairmen, Democrat Erskine Bowles and former Republican Sen. Alan Simpson, need 14 of the 18 members to support their proposal in order to issue a formal recommendation, which could then be voted on by Congress before the end of the year.

The commission’s vote is largely symbolic but will go a long way toward determining how, and how quickly, the U.S. might start addressing its ballooning national debt.

Precise details of the changes couldn’t be learned. Broadly, they are designed to incorporate suggestions made by some of the members of the National Commission on Fiscal Responsibility and Reform. Some aides spent much of last week trying to hone ideas and gauge potential support, with members communicating by cellphone.

Several Republicans on the panel have privately pushed for more spending cuts and other changes to tax policy. One of their concerns: the changes to the tax code, which would raise the amount some pay, are permanent, while many of the spending cuts are temporary. Democrats, for their part, want more cuts from defense appropriations.

The co-chairmen have spent days trying to determine if they can incorporate the ideas to win broader support ahead of Wednesday’s vote. Several people familiar with the process said it was still impossible to gauge the outcome.

Earlier this month, Messrs. Bowles and Simpson proposed a series of changes to U.S. spending and tax policy that would hold down the growth of the federal debt by roughly $3.8 trillion by 2020. They included changes to Medicare, Social Security, defense spending and other areas. The current national debt is roughly $13.8 trillion. Notably, they proposed lowering income tax rates while eliminating certain tax breaks for the middle class, including the ability to deduct the interest paid on mortgages.

The panel meets publicly Tuesday and plans a final vote Wednesday. Winning 14 votes appears unlikely given the political makeup of the committee, people familiar with the matter said. Nonetheless, a proposal that wins 10 votes and one that wins just five could send different signals to the country and to investors about how Washington might tackle the country’s worsening debt.

If the panel wins close to a dozen votes for its proposal, some of the ideas could be incorporated into the White House’s 2011 budget proposal, or tax and spending plans from either Democrats or Republicans next year. If the proposal receives only a handful of votes, it will likely send a signal that the parties remain at odds over how best to rework the country’s tax and spending priorities, suggesting that it will take much longer for any changes to be made.

A key threshold for the co-chairmen will be whether they can get the support of the 10 lawmakers on the panel who are returning in January as part of the new Congress.

Failure to win support from any of these members — who include likely chairman of the House Ways and Means Committee Rep. Dave Camp (R., Mich.) and the second-ranking Democrat in the Senate, Sen. Richard Durbin of Illinois — would show how difficult it might be for any proposal to win support from the politicians who would ultimately be charged with setting any plan in motion.

If those lawmakers vote for the plan, and withstand the political blowback from constituencies poised to defend their cherished programs, others on Capitol Hill could feel under pressure to act. Aides familiar with the matter said panel member Sen. Tom Coburn (R., Okla.) had expressed the most interest in forging a bipartisan deal.

Democrats and Republicans have both said the debt has put the U.S. on an unsustainable path that needs to be corrected.