Debate over a plan to repeal the Affordable Care Act seemed to have GOP lawmakers increasingly frazzled Tuesday, even as the White House stepped up a charm offensive and rumors of a compromise package percolated across Capitol Hill.

U.S. Sen. Tom Cotton (R-Ark.) avoided reporters who greeted him as he made his way from his office building to the Senate floor late Tuesday afternoon.

The White House also admitted on Tuesday that it is working on a “manager’s amendment” process with congressional leaders.

Earlier in the day, Cotton told radio talk-show host Hugh Hewitt that House Speaker Paul Ryan’s plan for a “three-step” process to repeal Obamacare was political fantasy.

“Hugh, there is no three-phase process. There is no three-step plan,” Cotton said. “That is just political talk. It’s just politicians engaging in spin.”

Cotton was dissing the theory that the Trump administration can strike down a large number of Obamacare regulations in “Phase 3,” using the statutory power of Health and Human Services Secretary Tom Price.

Then Republicans would use “Phase 3” to repeal all the aspects of Obamacare they could not get to in the first two phases.

Cotton’s critical remarks rocked Washington Tuesday morning. White House press secretary Sean Spicer was asked about Cotton’s comments at Tuesday’s afternoon press briefing. It’s unclear if the Trump White House reached out to Cotton to ask him to tone it down, but Vice President Mike Pence indicated earlier in the day he would be personally meeting with Cotton.

The Big Deal
The real intrigue is what the Trump White House is going to offer Cotton and the conservative members of the House of Representatives in open rebellion about the repeal bill, to work out a compromise.

The American Health Care Act, as the repeal bill is known, is in a state of flux, ranging from guaranteed to pass to dangerously close to being killed — depending on who you ask.

Right now, the bill looks like a long shot in the chamber where it originated. And on Monday, the Congressional Budget Office made things worse by unleashing a blisteringly negative forecast on its impact.

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The CBO claimed Monday that 14 million more Americans would be uninsured in 2018, a number that would grow to 24 million by 2026. The CBO bases that number on the GOP’s plan to drop the hated Obamacare mandate, which penalizes taxpayers without health care.

But the uninsured number is a powerful talking point, even though Republicans should know better, after having talked down the mandate for seven years. On Tuesday, another House Republican ran from the AHCA on those grounds.

Rep. Ilena Ros-Lehtinen (R-Fla.) said she could not support the AHCA because it would leave too many uninsured. On Monday, Rep. Rob Wittman (R-Va.) said the same.

Sen. Bill Cassidy (R-La.) said low-income Americans who are near Medicare eligibility won’t be able to afford health insurance under the GOP plan. The possible loss of Cassidy on the proposal, a doctor, is fresh evidence many across the conservative spectrum in the GOP have major concerns the plan does not include reform to major cost-drivers in the health care system — reforms that could make or break the affordability of insurance in a more free market system.

Overrule the Parliamentarian
Meanwhile, U.S. Sen. Ted Cruz (R-Texas) agrees with Cotton that the three-phase strategy is an illusion.

Cruz told LifeZette after a Senate vote that Republicans should dump all of the Obamacare repeal into a budget reconciliation bill, which cannot be filibustered, and pass it. If the Senate parliamentarian overrules the move, Vice President Mike Pence, as Senate president, can override it.

Republican Senate leaders seem loath to set that precedent, which would essentially get rid of the filibuster on many or all issues that come before the Senate.

A top Senate Republican leader told LifeZette that ultimately, the AHCA will be passed, as Republicans will not want to go home to their districts and explain to conservative constituents that they failed to repeal Obamacare.

The source also said the tax credits are likely the best issue to use in amendments to the AHCA to attract rebellious members of the conservative House Freedom Caucus, who could command as many as 30 votes in the House.

At the White House, a major charm offensive is underway to attract conservative votes. Trump is reportedly having pizza dinners with House members and taking them to the White House bowling alley.

The White House also admitted on Tuesday that it is working on a “manager’s amendment” process with congressional leaders.

Basically this means Trump is pushing congressional leaders to work out a grand bargain on amendments to the bill to nullify its critics. One idea is to speed up Medicaid entitlement reform. The AHCA would cut more than $880 billion out of Medicaid over 10 years, an item that Senate leaders believe should attract fiscal conservatives.

For now, the gloves stay on. Trump reportedly told House GOP leaders he would support 2018 primary challengers to Republicans who vote against the AHCA. But Spicer wouldn’t confirm the hardball strategy when LifeZette asked about it at Tuesday’s White House press briefing.

Senators were optimistic the bill would pass. In the end, the bill is still a “work in progress,” according to U.S. Sen. Pat Toomey (R-Pa.), who said a number of amendments could be offered.

“I think we’re going to get there,” said Toomey.