President Donald Trump attends a lunch meeting with members of Congress at the Cabinet Room of the White House in Washington, June 13, 2017.

President Donald Trump on Tuesday said a new Republican bill to repeal and replace major parts of Obamacare will come "as soon as we can do it."

Trump, after a lunch meeting with Republican senators whom he hopes will back the bill that is now being crafted in the Senate, said, "The results are going to be fantastic, and hopefully they'll be announced at the appropriate time."

"From day one I've said, 'We're going to repeal and replace Obamacare,' and that's what we're going to do," Trump said at the White House.

The president's remarks to reporters while sitting with the group of 13 senators he had lunch with followed what has become a pattern for him: bashing Obamacare at length, while not releasing details about what a Republican proposal will be to replace it.

Senate Republicans likewise have not disclosed what is in, or likely to be in, their bill.

Trump cited the fact that as many as one out of every three U.S. counties may not have more than just a single insurer selling Obamacare plans in 2018, and that premium prices for individual health plans have increased significantly in a number of states.

"Insurers are fleeing the market," he said.

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The president said the Affordable Care Act had failed to fulfill the claims by its supporters that the law would allow customers of health plans to keep their current doctors, or that their health costs would decrease.

"Obamacare has been broken. It's a broken promise," Trump said.

The House of Representatives last month passed, by a margin of just a single "yes" vote, the American Health Care Act, the Republican-backed bill to reform Obamacare.

But since then, a group of Senate Republicans has been drafting its own bill, amid concerns that the House legislation would lead to too much disruption in the health insurance markets.

The nonpartisan Congressional Budget Office estimated that 23 million more people would become uninsured by 2026 if the bill became law than would be the case if Obamacare remained as is.

Although Republicans hold majorities in both chambers of Congress, they have struggled to achieve the consensus among their caucus needed to pass an Obamacare replacement quickly, after years of promising to do just that.

The majority party includes conservative members who want either a total or faster repeal of the ACA. But it also includes more moderate members who are worried about a bill that would result in larger numbers of uninsured people, higher premiums for older people and rural residents, and defunding of Planned Parenthood.

"The House passed a bill, and now the Senate is working very hard, specifically the folks in this room, to come up with a bill that's going to be phenomenal," Trump said at the White House. "They'll come out with a real bill, not Obamacare."

Trump blasted Democrats as being obstructionists in the effort.

"If we came up with the greatest health-care plan or tax cut ... in our country's history, we couldn't get one Democrat vote," the president said.

Finance Committee Chairman Sen. Orrin Hatch, (R-Utah), reportedly said he does not expect the Senate's Obamacare replacement to be publicly disclosed this week.

"I think we've got a little ways to go," Hatch said. "There's a lot of things that have to be resolved."

Republicans reportedly would like to vote on their bill in the Senate before the July 4 recess.