By Amanda Becker and Susan Cornwell

WASHINGTON (Reuters) - President Donald Trump pushed Senate Republicans on Wednesday to take another stab at repealing Obamacare, calling all 52 Republican senators to the White House to urge them to keep their campaign promises and find a new healthcare approach.

"They MUST keep their promise to America," Trump wrote on Twitter ahead of the meeting, a day after the seven-year quest to repeal and replace Democratic former President Barack Obama's signature healthcare law collapsed in the Senate.

"The Republicans never discuss how good their healthcare bill is, & it will get even better at lunchtime," the Republican president tweeted. "The Dems scream death as OCare dies!"

Senate Majority Leader Mitch McConnell vowed to go ahead with a vote early next week on a repeal of the Affordable Care Act, popularly known as Obamacare, despite indications it will fail after the defections on Tuesday of at least three Republican senators.

"This is the same legislation that a majority of the Senate voted to send to the president in 2015," McConnell said on Wednesday on the Senate floor.

In that 2015 vote, Susan Collins of Maine - one of those who have announced opposition to repeal this time, along with Lisa Murkowski of Alaska and Shelley Moore Capito of West Virginia - was the only Republican to oppose the measure. Obama vetoed the repeal.

"Now we, thankfully, have a president in office who will sign it. So we should send it to him," McConnell said.

With Democrats united in opposition to repeal, McConnell can only lose two votes from his 52-48 majority in the 100-seat Senate to pass healthcare legislation.

Capito, speaking to reporters on Wednesday, expressed some doubts the Senate vote on a repeal-only healthcare bill would actually occur next week. "It’s changing so quickly," she said.

"I think we're probably going to air what our differences are again. The president has taken a lot of time to try to call us all individually," said Capito, who will attend the lunch. "I don't think anyone's mind is going to get changed sitting right there, but it gives us a chance to frame it where we have our differences."

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'HAVE TO HONOR PROMISE'

Repealing and replacing Obamacare was a top campaign promise for Trump and Republicans in Congress, who say it is a costly intrusion into the healthcare system.

But the reality has been difficult for a party divided between moderates concerned the Senate bill would eliminate insurance for millions of low-income Americans and conservatives who want to see even deeper cuts to Obamacare, which boosted the number of Americans with health insurance through mandates on individuals and employers, and income-based subsidies.

"We have to honor our promise," Republican Senator Ted Cruz told reporters. "For seven years Republicans have told the voters, if you elect us, we’ll repeal Obamacare. I think we will look like fools if we can’t deliver on that promise."

Republican Senator Orrin Hatch said it was a tough issue for Trump, but "I suspect he could be a little bit more forceful and I hope he will be. I think he needs to."

Democrats, clearly delighted with the turn of events, have welcomed the Republicans' failure to replace Obamacare as an opportunity to work together. Republicans conceded their other options may be exhausted.

The No. 2 Senate Republican, John Cornyn, told reporters it was "unfortunate" that he expected bipartisan talks to begin.

"Democrats are strongly committed to Obamacare and are unwilling to admit structural problems, which create the problems we are having in the individual market today," Cornyn said. "But we'll do the best we can with the hand we've been dealt."

If senators try to shore up Obamacare, an initial hurdle in coming weeks will be boosting faltering state insurance markets by ensuring that insurers keep receiving subsidies that help lower the cost of insurance for low-income individuals.

The Trump administration will continue making the subsidy payments through August while a related Republican lawsuit is pending. The uncertainty beyond that has rattled insurers.

Republican senators have acknowledged the need to address the unstable markets but resisted Democratic calls to fund the subsidies without accompanying reforms, calling it a "bailout" for insurance companies.

Funding for the Children's Health Insurance Program, a part of the Medicaid government health insurance program for the poor and disabled, known as CHIP, expires on Sept. 30 and will require reauthorization.

Bills to address the subsidy payments and CHIP would likely require 60 votes for passage, acting as a barometer of how inclined Republicans and Democrats are to work together, industry lobbyists and experts said.

Trump suggested on Tuesday that Republicans should allow the insurance markets to fail before working with Democrats. But Republican Senator Lamar Alexander, the head of the Senate Committee on Health, Labor and Pensions, said he would begin holding hearings on the issue in the next few weeks.

(Writing by John Whitesides; Additional reporting by Richard Cowan, Yasmeen Abutaleb and Susan Heavey; Editing by Mary Milliken and Jonathan Oatis)