Washington (CNN) The White House and Republican leaders struggled to extricate themselves from a political hole Tuesday after a non-partisan report warned that 24 million people would be uninsured over the next 10 years under the Republican plan to repeal Obamacare.

The report detonated controversy that risked damaging the push to quickly pass the bill and threatened the viability of the complex process envisioned for eventually constructing a replacement system.

"The headlines are terrible," said one senior GOP source involved in the health care process, describing the Congressional Budget Office's conclusions.

Sen. Bill Cassidy, a Louisiana Republican, struck out at the White House amid the political tumult whipped up by the report, that was published on Monday and also warned 14 million people could be without insurance by next year.

"That's not what President Trump promised," Cassidy, R-Louisiana, told CNN. "That's not what Republicans ran on."

Texas GOP Sen. John Cornyn described the difficulties of drawing up a bill that could placate conservatives in the House and unite more moderate Republicans in the Senate.

"It's like Goldilocks and the three bears, not too hot, not too cold, but just right," Cornyn said. "That's what we're trying to achieve."

Amid the rising concern on Capitol Hill, it was left to White House spokesman Sean Spicer to try to restore the lost momentum. He argued that there was simply no choice but to embrace the House bill.

"This is the only vehicle that seeks to achieve what people on our side have been talking about since 2010. This is it," Spicer said, referring to the bill that is currently being considered in the House and is known as the American Health Care Act.

"If we don't get this through the goal of repealing Obamacare and instituting a system that will be patient centered is going to be unbelievably difficult. This is the vehicle to do that," Spicer added.

Spicer said White House was working with the House leadership to draw up a large amendment to the bill that could include a number of smaller changes to the legislation -- perhaps to placate conservatives who are worried that the reform drive does not go far enough.

"We are obviously in talks with House leadership," Spicer said. "As I mentioned, the president will be on the phone with Speaker Ryan and Leader McCarthy to talk about some of these ideas and some of the paths forward. That is part of the legislative process."

"This has never been a take-it-or-leave-it," he added.

But a House GOP leadership aide told CNN that significant changes in the House bill are not planned and were not being negotiated. While there may be technical changes or minor substantive changes made before the bill reaches the House floor, the central components of the plan -- and Ryan's strategy -- stand unchanged, the aide said.

The issue of the CBO report was particularly problematic for Trump because he promised during his campaign that everyone would have health insurance. Spicer said that position had not changed. And he argued that the CBO had been "consistently wrong" in assessing the outcome of health care legislation fights.

The analysis has exacerbated divisions in the Republican Party cleaved by the health care debate, which has deep political implications for the credibility of President Donald Trump's young presidency and for the leadership of House Speaker Ryan.

The CBO score also appeared likely to complicate the calculations of moderate Republicans in the Senate where the legislation faces a much more difficult path to passage than in the House. And it emboldened Democrats, giving them a gift-wrapped talking point to support their defense of the Affordable Care Act.

'There is no three-step plan'

One prominent Republican senator, Tom Cotton of Arkansas, argued that the kerfuffle over the CBO score underscored the flaws of the current GOP approach in trying to repeal and replace Obamacare in a three step process.

"There is no three-step plan. That is just political talk. It's just politicians engaging in spin," Cotton, who has been calling on Republican leaders to slow the rush to pass the repeal bill, told Hugh Hewitt on his radio show.

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Cotton warned that the second step of the process -- the act of rewriting regulations by Health and Human Services Secretary Tom Price -- would be at the whim of the courts. The third step -- passing a replacement bill with Democratic support to get 60 Senate votes -- would also be problematic, he said.

"If we had those Democratic votes, we wouldn't need three steps. We would just be doing that right now on this legislation altogether. That's why it's so important that we get this legislation right, because there is no step three. And step two is not completely under our control," Cotton said.

Alabama Republican Rep. Mo Brooks, who supports the repeal of Obamacare, similarly warned that the project could be in peril.

"The legislation is definitely in serious trouble," the Alabama Republican told CNN's John Berman Tuesday.

JUST WATCHED Price: We disagree strenuously with CBO report Replay More Videos ... MUST WATCH Price: We disagree strenuously with CBO report 01:11

White House on defense

White House officials mounted a staunch defense of the House bill Tuesday, out-and-out rejecting the CBO score which undermines Trump's campaign trail promise that everyone would have health care.

"We're not pulling the rug out from anybody," said White House budget director Mick Mulvaney on CNN's "New Day," arguing that many people covered by Obamacare could not afford their deductibles or premiums, a factor that disguises the problems with the existing system.

"They have programs now that they can't get to the doctor with," Mulvaney said, on a snowy morning in Washington.

"According to the CBO, it's sunny and 75 degrees this morning ... The CBO is terrible in counting coverage," he added.

Price went on NBC's "Today Show" and argued that the Republican plan will actually increase the ability to patients to get insurance, making a distinction critics say is a semantic argument that ignores the human cost of changing health care plans.

"Every American will have access and have the financial feasibility to purchase it," he said.

Other Republicans argued that since the GOP health care plan dispenses with the individual mandate requiring everyone to buy insurance, it was not surprising that the raw numbers would look bad.

But they also acknowledged the political reality that the CBO report will have an impact on the wider debate about replacing Obamacare.

"I think we knew this would be a bad number," the senior GOP source said, describing the CBO analysis as "probably a low point in this whole process."

"But when you consider that we're taking away the mandate, it's to be expected."

GOP leaders remain hopeful about the process but are more realistic now on the political road ahead, the source added. "Obviously the situation could deteriorate. But I still think we get this done."

JUST WATCHED CBO report: 14 million more uninsured next year Replay More Videos ... MUST WATCH CBO report: 14 million more uninsured next year 02:33

GOP divisions

The fallout of the CBO report looked set to widen divisions among Republicans. House conservatives, for instance, see the plan's provisions to replace subsidies with tax credits to allow poorer Americans to buy care as "Obamacare Lite."

They also want to complete the roll back the expansion of Medicaid more quickly than the 2020 date envisioned by Ryan.

But more moderate Republicans, including governors of states that accepted federal funds to widen Medicaid access, are worried that a quicker contraction of the system could end coverage for millions of people.

There were also new suggestions of antagonism between rival factions of the Republican Party after the emergence of audio of Ryan saying in October that he is "not going to defend Donald Trump -- not now, not in the future."

Ryan apparently made the remarks in a private conference call with House Republican members following the release of an audio clip in which Trump could be heard bragging about sexually assaulting women.

Though Ryan's comments were reported at the time, the audio hadn't surfaced until it was published by the right-wing site Breitbart News Monday, making the timing of its release when Ryan was under political stress significant.

The site was previously run by Stephen Bannon, who is now Trump's chief strategist in the White House.

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Democrats on offense

Democrats, who understand well the hideously complex task of reforming health insurance markets after the Obamacare debate, quickly launched counter-attacks following the release of the CBO report.

"Americans will die if this legislation is passed and we have to do everything that we can to see that it is defeated," former Democratic presidential candidate Sen. Bernie Sanders said.

Senate Democratic Minority Leader Chuck Schumer said that Obamacare is becoming an asset -- not a liability -- for Democrats, even those running in red states that Trump won in November.

The CBO report found that 24 million more Americans would be uninsured by 2026 under the House Republican health care bill than under Obamacare, including 14 million by next year.

It also concluded that 14 million fewer people would enroll in Medicaid by 2026 under the GOP legislation compared to under Obamacare. And while premiums on average are expected to decrease, there would be a steep premium hike for older people with lower incomes.

A 64-year-old making $26,500 would pay $1,700 for coverage in 2026 under Obamacare, thanks to its subsidies -- but under the Ryan plan, that person would get hit with a annual premium bill of $14,600.

In total, an estimated 52 million people would be uninsured by 2026 under the GOP plan, compared to 28 million who would lack insurance under the current law.