House Republican leaders predict that a patients' rights bill passed in the Democratic-run Senate last week will fail in their chamber and that a GOP version is one that President Bush could sign.

Speaker Dennis Hastert, R-Ill., said Sunday that he and other Republicans would not try to block a vote on a House bill similar to the Senate's, but he offered more hope for a GOP plan that "will be much more balanced."

The Senate version, approved 59-36 Friday with nine Republicans in support, would increase the number of Americans without health insurance coverage because employers might drop for fear of lawsuits over medical decisions, Hastert contended.

The House's second-ranking Republican, Majority Leader Dick Armey of Texas, urged Senate Majority Leader Tom Daschle, D-S.D., to compromise and work with the GOP to produce a bill Bush will sign. Daschle said Democrats already have compromised "a good deal."

The Senate bill promises new health care protections for millions of Americans and offers them the ability to sue their health maintenance organizations.

Bush, who already had threatened a veto, said in a statement after the vote that he "could not in good conscience sign this bill because it puts the interests of trial lawyers before the interest of patients."

Hastert said the plan in the House is "to bring up a bill that I think is a better bill."

"I don't think the Senate version will pass," he said on CBS' "Face the Nation."

Daschle said he hopes that if Bush will not sign the Senate bill, he would let it become law without his signature. He noted that when Bush was governor of Texas, he allowed much of that state's patients' bill of rights to become law without signing it.

"Clearly, this has to become law. We've waited long enough. We've compromised a good deal," Daschle told ABC's "This Week."

Democrats and Republicans agree on the need for protections for people denied necessary medical care. They disagree on how to do that.

Democrats believe patients should have the right to sue insurers in state courts and that there should be no limit on the amount of money sought for lost wages, pain and suffering or punitive damages -- unless a state's law imposes them.

In federal court, the Democratic bill sets no limits for losses of wages, pain and suffering and has a $5 million cap on punitive damages.

Republicans argue that the Democratic bill would increase the costs of health care, enrich trial lawyers at the expense of patients and cause employers now offering insurance to their workers to drop the coverage for fear of becoming a lawsuit target.

They also say that under their bill, which requires patients to appeal their case to a review board before suing, people will get quicker results and the life-sustaining treatment they need.

The Republican House bill generally would keep lawsuits in federal courts and cap punitive damages at $500,000, but would, in certain circumstances when an insurer continues to deny treatment after a review board approves it, allow patients to sue in state court.

Armey told CNN's "Late Edition" that Daschle "should compromise and recognize that he can work with the House and get to the president a bill the president can sign."

Two years ago, the House passed a patients' rights bill similar to the Senate's with 68 Republicans and an independent joining 206 Democrats.