Washington (CNN) A slew of House conservatives are beginning to publicly oppose a draft of the Republican Obamacare repeal bill that was leaked last week, presenting a serious roadblock to the GOP's increasingly complicated efforts to dismantle the Affordable Care Act.

Republican Rep. Mark Meadows, the chairman of the conservative House Freedom Caucus, told CNN on Monday that he cannot support a draft of the GOP Obamacare repeal bill unless substantial changes are made.

Hours later, Rep. Mark Walker, the chairman of the Republican Study Committee, announced that he, too, could not support the leaked version of the legislation.

By Tuesday morning, others were also openly airing their concerns. As he exited a House conference gathering, GOP Rep. Mark Sanford — the author of an alternative Obamacare repeal and replacement bill — told CNN that he could not support the legislation "in its present form." GOP Rep. David Brat, meanwhile, said that the majority of the Freedom Caucus would vote against the draft bill.

The mounting opposition come as top House Republicans are preparing to unveil legislation to repeal major portions of Obamacare and are struggling to bridge deep divisions within their own conference.

Meadows told CNN that what is unacceptable to him are the refundable tax credits included in the draft of the bill. Those tax credits, the North Carolina congressman said, are nothing short of an "entitlement program."

"What is conservative about a new entitlement program and a new tax increase? And should that be the first thing that the President signs of significance that we sent to the new President?" Meadows said in an interview. "A new Republican president signs a new entitlement and a new tax increase as his first major piece of legislation? I don't know how you support that -- do you?"

The congressman also took issue with the way the tax credits would be given out, arguing that it would make some wealthy individuals eligible.

"So the headline is that the GOP is reducing subsidies to needy individuals when in fact, the growth of the taxpayer-subsidized reimbursements will actually increase. The total dollars that we spend on subsidies will be far greater," he said. "So you can be a millionaire and not have employer-based health care and you're going to get a check from the federal government -- I've got a problem with that."

Asked whether the concerns were widespread within the Freedom Caucus, Meadows said plenty of others share his concerns and would also be willing to vote against the GOP Obamacare repeal bill -- though he declined to predict how many would be willing to draw a line in the sand.

Walker echoed Meadows, saying the draft bill "contains what increasingly appears to be a new health insurance entitlement with a Republican stamp on it."

"The draft legislation, which was leaked last week, risks continuing major Obamacare entitlement expansions and delays any reforms," Walker said in a statement. "It kicks the can down the road in the hope that a future Congress will have the political will and fiscal discipline to reduce spending that this Congress apparently lacks."

Walker said he would encourage other members of the Republican Study Committee to oppose the bill.

House Speaker Paul Ryan tried to downplay the rifts within his own party at a news conference Tuesday morning, insisting that there were no "rival plans" and that the House, Senate and White House are all working together.

"I feel at the end of the day when we get everything done and right, we're going to be unified on this," Ryan said.

And a senior GOP aide reacted with this statement: "Tax credits have long been a part of Republican health care plans, including the one authored by now-Secretary (Tom) Price that had broad support from members of the (Republican Study Committee) and Freedom Caucus."

A draft of the House Republican bill to repeal Obamacare obtained by CNN last week would replace the law's subsidies with less generous tax credits, increase the amount insurers could charge older Americans and more or less eliminate Medicaid for low-income adults.

The refundable tax credit would be given out based on age and range from $2,000 for those under 30 to $4,000 for those between ages 60 and 64.

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The legislation was dated two weeks ago as of Friday, but a Republican source said the most updated version remains in the "same ballpark" as the draft. The bill is expected to be released sometime next week, according to leadership sources.

By Tuesday afternoon, multiple GOP aides indicated that no major changes had been made to the GOP draft bill. In a staff-level meeting Tuesday morning between the House Freedom Caucus and GOP leadership, aides announced no major changes to the leaked legislation and that it remained the same on the refundable tax credits and Medicaid fronts, according to a source.

GOP divisions

Meadows' opposition to the draft bill illustrates one of many divisions that have come to light within the GOP over repealing and replacing Obamacare.

Plenty of Republican lawmakers have expressed reservations about moving too quickly on repeal without a clear alternative to the Affordable Care Act. Others, including members of the Freedom Caucus, are agitating for GOP leaders to take up a 2015 version of an Obamacare repeal bill that was vetoed by President Barack Obama.

To quell widespread concerns, GOP leaders earlier this year committed to including "replacement" measures in the Obamacare repeal bill -- a move that has seriously complicated the crafting of the legislation.

Republican Rep. Jim Jordan, another member of the Freedom Caucus, told CNN on Monday that he also has serious reservations about the repeal bill. He would not comment on how he would vote until he has seen a draft of the final measure.

"We didn't promise the American people that we would repeal it, except we're going to keep Medicaid expansion. We didn't promise the American people except we're going to keep some of the tax increases in it. We certainly didn't promise the American people we're going to repeal it but we're going to start this whole new entitlement called advanced refundable tax credits," Jordan said. "I think this is the wrong thing to do."