Does President Trump have what it takes to reunite a fractured Republican party? This week could offer some clues.

The president is set to reveal his fiscal budget for 2018 on Thursday, potentially deepening existing divides between GOP lawmakers in the Republican-controlled Congress. Proposed increases in military spending and cuts to discretionary domestic programs, while expected to elicit cheers from conservative Republicans, have many moderate Republicans caught between a rock and a hard place: oppose the president, or support reductions to popular programs such as aid for disabled children?

The budget comes as Republicans prepare Monday for a Congressional Budget Office analysis of the "repeal and replace" healthcare plan. The CBO is expected to conclude that fewer Americans will have health coverage under the proposal despite Mr. Trump's earlier vows of "insurance for everybody" – a conclusion that will likely affect the chances of the proposal passing.

Some GOP lawmakers are urging House conservatives not to back the healthcare plan or big spending cuts, as they are likely to face rejection in the Senate, where Republicans hold a slimmer majority. Supporting the president on these matters, some say, could result in a backlash against House Republicans in the 2018 congressional elections.

"Do not walk the plank and vote for a bill that cannot pass the Senate and then have to face the consequences of that vote," said Tom Cotton (R) of Ark. on ABC's "This Week." "If they vote for this bill, they're going to put the House majority at risk next year."

To see conservatives in a GOP-controlled Congress blocking a Republican president is rare, but not unprecedented, as Francine Kiefer reported for The Christian Science Monitor in December:

It’s unusual for lawmakers on the president’s team to actually block him when their party holds both chambers of Congress and the White House. But it’s not unheard of. Republican George W. Bush could not get immigration reform through the House when he tried it. And plenty of Democrats defected on health care under Bill Clinton. Further back, Democrats refused to let Franklin D. Roosevelt pack the Supreme Court. If Democrats hang together, it would take only three Republicans to deny Trump a majority, not to mention the 60-vote threshold required for most major Senate business.

House conservatives have vowed to block the Trump-backed healthcare legislation, denouncing it as a form of "Obamacare Lite." The proposed plan would eliminate the current mandate that nearly all people in the US carry insurance or face fines. It would also use tax credits to help consumers buy health coverage, phase out an expansion of Medicaid and cap the program for the future, expand health savings accounts, scrap a number of taxes, and end some requirements for health plans under the Affordable Care Act.

Some House conservatives, such as Rep. Jim Jordan (R) of Ohio and other members of the House Freedom Caucus, say they oppose the proposed refundable tax credits as a new entitlement that will add to government costs and would allow Medicaid to be phased out more quickly. Other more moderate Republicans, such as Gov. John Kasich of Ohio, argue that the plan needs to allow for continuing Medicaid coverage for the poor.

The debate over the future of Medicaid highlights divisions in the party in recent months as Republicans grapple with how best to repeal and replace the Affordable Care Act, which they have long railed against. As Ms. Kiefer reported for the Monitor in January:

For years, Republicans have been united in their goal to repeal Obamacare, attempting to kill or alter the law more than 60 times. But they haven’t been able to unite around a replacement that gives people more freedom to make their own health choices while covering the 20 million Americans who currently get health insurance under the Affordable Care Act. That's in addition to fixing the skyrocketing premiums and shrinking choices in the law’s insurance marketplaces. Might the outsider president-elect be able to lead them out of this thicket?

With a potential fight brewing over budget cuts, that task could become considerably more challenging.

"What I told him is that when we get in a deadlock between the House and the Senate, different factions of the party ... you're the guy who needs to come down and close the deal," said Sen. Lindsey Graham, following a White House lunch with Trump on Tuesday, to Reuters.

For now, in an effort to win over members of the House Freedom Caucus on Trump's legislative agenda, budget director Mick Mulvaney has invited the conservative lawmakers to a bowling and pizza night at the White House on Tuesday.

But ultimately, says Rep. Tom Cole of Oklahoma, the fate of the budget is in Congress's hands.

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"At the end of the day, we’ll have a budget. We’ll pass the budget," he told Reuters. "Our budget is not necessarily the president’s budget."

This report contains material from the Associated Press and Reuters.