WASHINGTON, July 31 — With House Republican leaders eager to schedule a vote this week on a patients' bill of rights, Congress and the White House haggled today over the biggest unresolved question: the right of consumers to sue health insurance companies and employers for treatment decisions that cause harm to patients.

The White House said it had made significant progress in negotiations with Congress, but supporters of the main bipartisan bill said major problems still had to be solved. Regardless of whether there is an agreement, House Republican leaders said they expected to take the issue to the House floor in the next few days, before Congress adjourns for a monthlong summer recess.

President Bush visited the Capitol today and discussed health care, education and energy legislation over lunch with Senate Republicans. After the meeting, Mr. Bush said he had narrowed the differences on patients' rights through negotiations in the last week with Representative Charlie Norwood, the Georgia Republican who has been leading a six- year effort to set strict federal standards for health maintenance organizations and insurers.

"We're making progress," Mr. Bush said. Referring to Mr. Norwood, the president said, "I'm hopeful that he will shake the hand of accommodation that I put out for him."

Ari Fleischer, the White House press secretary, gave an upbeat assessment of the negotiations.

"I think that it's fair to say that the nation is on the threshold of having a patients' bill of rights that can be signed into law," Mr. Fleischer said. "There is some additional work that does need to be done, but many of the differences that remain are easily bridgeable if others who are working with Congressman Norwood are interested in bridging those differences."

Mr. Norwood met today with the seven leading supporters of his legislation, including three senators who pushed a similar bill through the Senate in late June, despite a veto threat from Mr. Bush. The group formulated an offer, which Mr. Norwood said he would convey to the White House for review.

The legislation defines a wide variety of rights for people with health insurance, guaranteeing access to emergency care, medical specialists and clinical trials of new drugs. The negotiations now focus almost exclusively on the major sticking point: the right of patients to sue H.M.O.'s for injuries caused by the delay or denial of care.

Employers who provide health benefits to employees worry that they too will be named as defendants if Congress makes it easier to sue H.M.O.'s and insurance companies.

Mr. Norwood and the co-sponsors of his bill agreed to take steps to protect employers against lawsuits, but they refused to provide similar protection to H.M.O.'s and insurers.

Under their proposal to the White House, employers would be exposed to liability only if they directly participated in decisions to deny care to patients. The small group of companies that finance and administer their own health plans — companies like Caterpillar and Motorola — would have an extra protection: they could be sued only in federal court, not in state courts, which are often viewed as more friendly to plaintiffs.

Representative Robert E. Andrews, Democrat of New Jersey, said that under this proposal, lawsuits against H.M.O.'s would be tried in state courts, under state tort law.

"The Bush administration claims that its highest priority is the protection of employers," Mr. Andrews said. "Our proposal should satisfy that concern."

Another sponsor of the bipartisan bill, Representative Greg Ganske, Republican of Iowa, said, "We are making a very significant step toward the White House on a major issue of contention."

Sponsors of the Senate-passed bill agreed. Senator John Edwards, Democrat of North Carolina, said, "We have moved step by step toward the president." Senator Edward M. Kennedy of Massachusetts, the Democrats' senior strategist on health care issues, said, "Our proposal responds to the president's very legitimate concerns, and it ought to be the basis of a sound compromise."

Mr. Norwood said: "I'm going back to the White House to see if I can negotiate with them and bring the two sides together. This is my last hope to make a deal."

Continuing to apply pressure on the negotiators, the House majority leader, Dick Armey, Republican of Texas, said, "I would expect a vote on that subject before we adjourn" at the end of the week.

Mr. Norwood is the main channel of communication between Congress and the White House on patients' rights. That arrangement has frustrated some lawmakers.

Representative Marion Berry, Democrat of Arkansas, a main co- sponsor of Mr. Norwood's bill, said: "We need to talk to somebody who has the authority to do the deal. A representative of the White House has got to be in the room with us."

Mr. Norwood assured his co-sponsors that he was still solidly allied with them, that he wanted a bipartisan agreement and that he would not cut a separate deal with the White House.