(CNN) Republican lawmakers have finally unveiled a plan to repeal major portions of Obamacare, capping years of attacks against the health care law and a months-long debate that exposed deep rifts within the GOP.

Now comes the hard part.

House Republican leaders must begin in earnest the tough task of selling the new plan to overhaul America's health care system to colleagues in both chambers on Capitol Hill, where there is a myriad of clashing interests. And they will have to convince a skeptical public it's worthwhile, just seven years after Congress passed the Affordable Care Act.

The political ramifications couldn't be more significant. Perceptions that Republicans and President Donald Trump are not moving ahead with a wholesale Obamacare repeal would anger large swaths of the party's base, while the possibility of millions of Americans losing coverage could emerge as a top liability for Republicans ahead of the 2018 midterm elections.

Trump is expected to offer a more robust embrace of the House GOP health care plan Tuesday when he meets with the deputy whip team at the White House in the afternoon, an administration official told CNN Tuesday.

Whether Trump is committed to the political challenge of repealing and replacing Obamacare remains a central question.

"He'll work hard to get this done," the administration official said, including pushing reluctant conservatives by helping build support for this bill out in their districts.

That's one of the reasons Texas Sen. Ted Cruz was invited to the White House for dinner Wednesday night. He's among the skeptical conservatives who believe the new bill is essentially a new mandate.

In the coming days, key House committees will hold extended sessions to debate and revise a bill that until Monday night was closely guarded — including being held in a House office for lawmakers to view but not copy. These gatherings will provide plenty of opportunity for political grandstanding from Democrats as they look to cast Republicans as responsible for taking away people's health insurance.

The legislation unveiled Monday would scrap the individual mandate, a major pillar of Obamacare, replacing it with refundable tax credits for individuals to purchase health insurance. It would also restructure Medicaid and defund Planned Parenthood.

The proposal -- dubbed the "American Health Care Act" -- seeks to maintain Obamacare's protections for people with pre-existing conditions, but would allow insurers to charge higher premiums to individuals whose coverage has lapsed. The bill would also keep in place the so-called "Cadillac tax" on employers who provide generous health insurance plans.

Americans are virtually split on the individual mandate, with 48% favoring removing the requirement to obtain coverage or pay a penalty and 50% wanting to keep it, according to a CNN/ORC poll released Tuesday morning.

Other aspects of Obamacare are far more popular. A broad majority, 87%, support maintaining the law's protections for those with pre-existing conditions, and 61% are opposed to a replacement bill that would curb funding for the expansion of the Medicaid program.

Here are the political obstacles Republican leaders are about to confront as they attempt to get this bill through the House and Senate.

Millions stand to lose coverage

The real-world ramifications of repealing Obamacare are complicated to say the least.

But most health care experts agree on this much: Millions of Americans are likely to lose their coverage under the new GOP plan.

It will be a tough pill for many Americans to swallow seven years after the passage of the Affordable Care Act. The law has been highly controversial since its inception, but the reality is that some 20 million people gained coverage as a result of it -- particularly low-income Americans.

The most prominent Republican has already veered off-message on this front: Trump. While Trump wants to eliminate Obamacare, the President frustrated his colleagues when he promised earlier this year that the GOP plan would offer "insurance for everybody."

Tevi Troy, deputy secretary of Health and Human Services under President George W. Bush, said the GOP's top challenge is "meeting the expectations" on coverage.

"They need to maintain coverage levels so you won't have large numbers of people saying, 'I was covered under Obamacare and I'm not covered now,'" Troy told CNN.

Major sticking point: Medicaid expansion

The changes that House Republicans are proposing to make to Medicaid are not sitting well -- among some fellow Republicans.

Thirty-one states expanded Medicaid under the Affordable Care Act, extending coverage to some 11 million low-income adults. Drastically restricting that program would leave many of those people without coverage -- an outcome that has plenty of GOP governors and lawmakers on edge.

The plan would overhaul the whole program, which covers more than 70 million people, by sending states a fixed amount of money per enrollee, known as a per-capita cap.

GOP Sen. Lisa Murkowski said that her party must find a "fair and humane" way to treat those who gained coverage through Medicaid expansion.

"In Alaska, we've got 27,000 people that are now eligible for coverage that didn't have it before. Really have no place else to turn," Murkowski said. "And so I'm trying to figure out a way that treats these people in a fair and humane manner."

Sen. Orrin Hatch, the top Republican on the Senate Finance Committee, said the intra-party division over Medicaid was a "problem."

"The Democrats aren't going to help us. So it is a problem," Hatch told reporters moments before the House bill was released.

Conservative backlash

Conservative Republicans are not making things easy.

Their concern: The proposal doesn't go far enough in gutting Obamacare.

Over the past few weeks, GOP lawmakers like Sen. Rand Paul and members of the conservative House Freedom Caucus have raised hell over the draft bill, and it became clear Monday night that one provision they railed against -- refundable tax credits -- remains in the final draft.

Conservatives say the refundable tax credits amount to just another entitlement program.

"Still have not seen an official version of the House Obamacare replacement bill, but from media reports this sure looks like Obamacare Lite!" Paul tweeted Monday night.

Analysis on the bill circulated by staff for the Republican Study Committee, a group of fiscal conservatives zeroed in on the tax credits, referring to them as "a Republican welfare entitlement"

"Writing checks to individuals to purchase insurance is, in principle, Obamacare,"‎ the RSC memo, obtained from a GOP source, stated.

Meanwhile, conservatives may also have problems with other provisions of the bill, like the fact that the House plan won't scrap the Obamacare taxes until 2018 or the fact it preserves the Cadillac Tax -- which has never been implemented -- yet still has been a point of contention for Democrats and Republicans alike.

Freedom Caucus member Rep. Jim Jordan said cited specific frustration with the fact that the House bill would keep Obamacare taxes in place until 2018 instead of repealing them immediately like a 2015 repeal and replacement measure vetoed by President Barack Obama would have done.

"We put on President Obama's desk a bill that got rid of all the taxes and ... a Republican Congress is going to put on a Republican president's desk a bill that keeps taxes in place?" Jordan, R-Ohio, said.

House GOP leaders can only lose roughly 20 Republican votes when the bill comes to the floor later this month. Conservatives are under pressure from outside advocacy groups like Heritage Action and the Club for Growth and will be reluctant to support the bill unless their major areas of concern are addressed.

"The real debate going on between the House GOP is members who want to make substantial changes to the ACA but realize getting rid of it will be quite problematic and members who ... generally want to get rid of everything and go back to the way things were," said Andy Slavitt, former acting head of the Centers for Medicare and Medicaid Services. "It's not possible."

Over the course of the last few weeks, committee staff have gone back and forth with the Congressional Budget Office. While there was no official score, sources say the early returns for CBO weren't positive -- both in cost and in coverage. Many of the prominent shifts in the bill's language, in fact, were driven by GOP efforts to secure a better final score, sources said.

House bill won't fly in the Senate

House GOP leaders have coordinated with their Senate counterparts and insist they are largely all on the same page.

But House Speaker Ryan and Senate Majority Leader McConnell face different internal dynamics in their chambers, and a bill that can pass in the House is not necessarily a bill that can pass the Senate.

One potential holdup in the Senate will be over funding Planned Parenthood.

Many House conservatives and outside groups are worried that in the upper chamber, where Republicans hold a narrow majority, leaders will be forced to strip out the provision to defund the group to get support of more centrist GOP senators like Susan Collins of Maine.

Another issue that has split Senate and House Republicans is the proposed overhaul of the Medicaid program. Even before the House bill was released, four Senate Republicans -- Murkowski, Rob Portman of Ohio, Shelly Moore Capito of West Virginia, and Cory Gardner of Colorado -- of penned a letter to McConnell expressing concerns that the legislation would cut off those relying on Medicaid to address opioid addiction and mental health issues.

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"We believe Medicaid needs to be reformed, but reform should not come at the cost of disruption in access to health care for our country's most vulnerable and sickest individuals," the senators wrote.

House GOP aides point to the provision that grandfathers existing enrollees and allows them to keep their coverage. But it's unclear if the details in the House bill will address these concerns, which have the potential to derail the bill as it works its way through the legislative process.

How much will Trump help?

House Republican leaders will need all the help they can get in the coming weeks as they try to shepherd their Obamacare bill through Congress.

It's not clear whether that support will come from the White House. House GOP aides have repeatedly claimed they are working "hand in glove" with the White House, and over the course of the final harried days of drafting, that was true. There was deep involvement of several top executive branch officials over the weekend.

"House just introduced the bill to #RepealAndReplace#Obamacare. Time to end this nightmare," the message said.

Meanwhile, White House spokesman Sean Spicer said in a statement Monday night that the House bill was an "important step" in fixing the health care system -- but did not go as far as to offer a explicit or forceful backing.

And Tuesday morning, Trump was still qualifying his support for "our bill," saying it was out for "review and negotiation."