Democratic leaders had been contemplating an intricate legislative two-step, by which the House would approve the original Senate health care measure and both chambers would adopt a package of changes in a budget reconciliation bill. Both measures would then be sent to Mr. Obama for his signature.

Some officials said House leaders were holding out hope for a favorable ruling by the parliamentarians that would allow them to proceed as planned — or to circumvent the problem.

But Senator Kent Conrad, Democrat of North Dakota and chairman of the Budget Committee, said the reconciliation instructions in last year’s budget resolution seemed to require that Mr. Obama sign the Senate bill into law before it could be changed.

“It’s very hard to see how you draft, and hard to see how you score, a reconciliation bill to another bill that has not yet been passed and become law,” Mr. Conrad said. “I just advise you go read the reconciliation instructions and see if you think it has been met if it doesn’t become law.”