WASHINGTON -- House Democrats negotiating a rescue of Fannie Mae and Freddie Mac said they wouldn't exempt the proposal from the annual debt limit, a move designed to quell lawmakers' concerns that the Treasury's financial aid could be unlimited.

Rep. Barney Frank (D., Mass.) said any help for the two mortgage-finance giants would be counted against the federal debt limit, which Congress must vote to increase. Congress has voted five times during the Bush presidency to increase the limit on Treasury borrowings, which currently stands at $9.815 trillion. Total public debt subject to the limit as of July 15 is $9.440 trillion, within $375 billion of the limit.

Some lawmakers have worried the rescue plan would expose taxpayers to trillions of dollars in losses. Supporters of the plan have said that the Treasury may not have to spend any money and that the rescue effort is meant largely as a confidence-building move for markets.

Treasury Secretary Henry Paulson had sought to exempt the plan from the public-debt limit. That request "will not be honored," Mr. Frank said. House Budget Chairman John Spratt (D., S.C.) and Ways and Means Chairman Charles Rangel (D., N.Y.) were working with Mr. Paulson to find a compromise, Mr. Frank said. The Treasury didn't respond to requests for comment.

Mr. Frank, chairman of the House Financial Services Committee, said the move "deals with this ridiculous notion" that taxpayers could take a hit of trillions of dollars.

The change is the latest example of how lawmakers are diverging from the administration on the rescue plan, which is expected to see a House vote Wednesday as part of a larger housing-related package.

The decision on the debt limit is not without its risks; lawmakers don't relish having to vote to increase the limit on the country's debt. Still, including the debt-ceiling language could address the questions lawmakers continue to raise about the legislation. The overarching issues: How much help should the government make available and how can taxpayers be protected?

One safeguard both parties back is to make sure the government is paid back before the shareholders of the companies. In addition, lawmakers want the government to approve executives' salaries at Fannie and Freddie.

"On the Senate side, we appreciate the need to act on this quickly," said Sen. Jon Kyl (R., Ariz.), a member of party leadership. But there are few ways to protect the government, and taxpayers, from financial risk. "Inherent to this is taxpayer risk," Mr. Kyl said.

Mr. Frank told reporters that there were "no dealbreakers" left that could derail the bill, though he declined to go into details about what issues lawmakers and the Bush administration still have to reconcile. He did say that $3.92 billion in White House-opposed community-development block grants would be included in the legislation, despite a veto threat.

Mr. Paulson emerged from an evening meeting with lawmakers Thursday saying he is confident the negotiators "will come to a very acceptable result."

Write to Sarah Lueck at sarah.lueck@wsj.com

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