Even after bringing conservative Republicans on board with the revised American Health Care Act, Republican leadership was unable to garner enough support to bring the bill to the floor this week.

An amendment released Tuesday night, written by moderate Rep. Tom MacArthur, appeared to placate conservatives who did not think the original bill went far enough in its repeal of Obamacare, the law formally known as the Affordable Care Act.

But pushback from moderates seems to have stalled the bill.

After the amendment was released, the White House pushed for a vote on Friday or Saturday, making a last-minute play for a signature legislative win in President Donald Trump's first 100 days, but House leadership on Thursday night said a vote would not happen until next week at the earliest.

New provisions would allow states to apply for a waiver that would exempt their insurance markets from certain regulations created by Obamacare if they could prove it would lower costs.

Health-policy experts say the waiver could have negative consequences for people with preexisting conditions and allow insurers to offer plans that cover fewer health needs.

(Read more about the amendment »)

The tweak was enough to get the conservative House Freedom Caucus officially on board with the bill, which could mean support from about 20 representatives who opposed the original AHCA.

But the amendment may have alienated more moderate members of the Republican caucus and could leave the AHCA short of the votes it needs to pass. Up to 22 Republicans can vote against the bill for it to pass through the GOP-controlled chamber.

House Majority Leader Kevin McCarthy told reporters on Thursday night that a vote would not happen Friday or Saturday.

"We've been educating people on healthcare," McCarthy said. "It's not tomorrow. I never said it was going to be tomorrow. ... We are not voting on healthcare tomorrow."

MacArthur, a co-chair of the moderate Tuesday Group, told reporters earlier on Thursday that the Republican conference did not have enough votes.

Members of the House GOP conference who originally said they would vote "yes" have now expressed doubts about the amendment. Rep. Mario Diaz-Balart on Thursday said there were "a lot of red flags" in the legislation and that he was undecided. He was a "yes" on the first version of the AHCA.

According to HuffPost congressional reporter Matt Fuller's count, 17 Republicans are against the bill, 10 are leaning "no," and 11 are undecided.

Also complicating a vote on the bill was Democrats' insistence that they would oppose a funding bill to avoid a government shutdown if the GOP brought the AHCA to the floor at the same time.

The White House had sought to apply pressure ahead of Trump's 100th day in office, on Saturday. Mick Mulvaney, the director of the Office of and Management and Budget, told CNBC on Thursday that he was "still holding out" for a vote on Saturday.

House Speaker Paul Ryan has repeatedly said leadership would not bring the legislation to the floor until "we have the votes."

Passing the AHCA through the House would represent a significant hurdle cleared, but it would also lead to new challenges.

Several Republican senators have expressed doubts about the AHCA. And since Republicans are attempting to move the bill through the budget reconciliation process, it could be blocked in the Senate because of a rule that prevents such bills from containing measures that don't directly affect the federal budget.