While a House bill with a provision that could reduce federal aid to some Ivy League schools has stalled for the year, Congressional aides and Yale officials said they expect a renewed debate over the measure next year.

The legislation, introduced by the Republican leadership of the House Committee on Education and the Workforce, would have reshaped the formula for allocating financial aid that schools receive directly from the federal government, in addition to making key changes to policies concerning student loans and college accreditation. But with the bill unable to move out of committee and a new Congress convening next January, the future of those proposals remains uncertain.

By modifying formulas established in the 1970s, the bill’s supporters said they intended to reduce inequities in the campus-based aid system that favor older, wealthier schools. But Richard Jacob, Yale’s associate vice president for federal relations, said the University’s primary criticism of the changes in campus-based aid were in the amount of money being offered to schools under the bill, not how it was distributed.

“We are concerned about any proposal that would reduce the amount of federal need-based aid to Yale students,” said Jacob in an e-mail from Washington, D.C. “The shortage of funding for the campus-based programs, not the allocation formula, is the real issue.”

During the current academic year, Yale is estimated to receive about $3.9 million in campus-based aid. But while the proposed changes are expected to have a larger impact on other Ivy League schools, like Harvard, a new formula is unlikely to significantly cut Yale’s funding due to the University’s relatively high proportion of students eligible for need-based aid, University Director of Financial Aid Myra Smith said. In addition, campus-based aid programs — which include low-interest Perkins loans, work-study awards and supplemental grants for the neediest students account for only about 10 percent of Yale’s financial aid budget.

The effect on Connecticut under the proposed changes would likely be significantly less pronounced than in other New England states. According to an analysis by the American Council on Education, Connecticut colleges and universities would actually gain about $800,000 under the proposed changes, even as Massachusetts schools would lose a combined $9.4 million.

Staffers on both sides of the aisle in Congress said that the divisions preventing the bill from moving through the House extend well beyond campus-based aid, however, into a wide range of issues concerning federal oversight over higher education. The American Association of Universities — which includes Yale and 61 other top research universities — has criticized provisions requiring colleges to report more information about costs, instituting rules surrounding transferring credits between schools, and calling for schools to promote “intellectual diversity.”

But Alexa Marrero, a spokeswoman for Republicans on the House Education and Workforce Committee, said the campus-based aid provisions have created some opposition among schools that feel they would lose out under the bill.

“Generally speaking, this is a very basic issue of fairness,” Marrero said. “[But] in any type of debate where some schools and regions may gain and others may see a reduction in their funds, there’s always going to be some opposition.”

At the same time, although support for the bill has not been split entirely on party lines, some top House Democrats have argued that the bill should offer more new funding for both Pell Grants and campus-based aid.

“Their bill hasn’t moved forward because it is a bad deal for students,” said California Rep. George Miller, the senior Democrat on the House Committee on Education and the Workforce, through a spokesman. “I hope that my Republican colleagues will reconsider their legislation and, instead, work with us to draft a reasonable higher ed. bill that makes college more affordable for middle class families.”

Because the legislation proposed by House Republicans was part of an effort to complete the mandated reauthorization of the Higher Education Act, many of the proposals in this year’s legislation will almost certainly be reconsidered next year.

Jacob said Yale supported some provisions in the House Republicans’ bill, including an increase in limits on federally subsidized loans that could reduce the debt burden for professional students. But Jacob said he was not surprised the bill did not move through Congress, noting that he thought it was a “placeholder” for issues that will reemerge after elections next November.