WASHINGTON >> One key unsettled issue stalling progress on President Donald Trump’s big bill in Congress is particularly daunting: how to cut billions from health care without harming Americans or hospitals and others that provide care.

Republicans are struggling to devise a solution to the health care problem their package has created. Estimates say 10.9 million more people would be without health coverage under the House-passed version of the bill. GOP senators have proposed steeper reductions.

“The Senate cuts in Medicaid are far deeper than the House cuts, and I think that’s problematic,” said GOP Sen. Susan Collins of Maine.

Senators have been meeting behind closed doors and with Trump administration officials as they rush to finish up the big bill before the president’s Fourth of July deadline. Much of the package, with its tax breaks and bolstered border security spending, is essentially drafted. But the size and scope of health care cuts are among the toughest remaining issues.

Senate Majority Leader John Thune is determined to avoid that outcome, sticking to the schedule and pressing ahead with voting expected by the end of the week.

The changes to the federal health care programs, particularly Medicaid, were always expected to become a centerpiece of the GOP package, a way to offset the costs of providing tax breaks for millions of Americans. Without action from Congress, taxes would go up next year when current tax law expires.

The House-passed bill achieved some $1.5 trillion in savings overall, a large part of it coming from changes to health care. The Medicaid program has dramatically expanded in the 15 years since Obamacare became law and now serves some 80 million Americans. Republicans say that’s far too high, and they want to shrink the program back to a smaller size covering mainly poorer women and children.

House Democratic Leader Hakeem Jeffries said Republicans are “trying to take away health care from tens of millions of Americans.” Democrats are uniformly opposed to what they call the “big, ugly bill.”

Much of the health care cost savings would come from new 80-hour-a-month work requirements on those who receive Medicaid benefits, even as most recipients already work.

But a number of GOP senators, and the hospitals and other medical providers in their states, are raising steep concerns that the provider tax changes would decimate rural hospitals.

In a plea to lawmakers, the American Hospital Association said the cuts won’t just affect those who get health coverage through Medicaid, but would further strain emergency rooms “as they become the family doctor to millions of newly uninsured people.”

“And worse, some hospitals, especially those in rural communities, may be forced to close altogether,” said Rick Pollack, president and CEO of the hospital group.Trying to engineer a fix to the problem, senators are considering creating a rural hospital fund to help offset the lost Medicaid money.