Republican leaders sound more and more convinced that their plan to overhaul the American healthcare system will clear a huge hurdle this week.

Officials from Congress and the White House suggested over the weekend that the American Health Care Act — the GOP plan to repeal and replace Obamacare — would make it past the House of Representatives this week.

On CBS' "Face the Nation," President Donald Trump said he believed the House could have voted on the bill on Friday, but he told House leaders to wait.

"I think they could have voted on Friday," Trump said. "I said, 'Just relax. Don't worry about this phony 100-day thing. Just relax. Take it easy. Take your time. Get the good vote and make it perfect.'"

Vice President Mike Pence, when asked about Trump's accomplishments during his first 100 days on "Meet the Press," predicted that while the healthcare overhaul didn't happen before the milestone, it would soon.

"But he's signed 30 different executive orders on virtually every one of those topics that you just referred to," Pence said. "And we’re working with the Congress. I think healthcare reform, repealing and replacing Obamacare is just around the corner."

And House Majority Leader Kevin McCarthy, who schedules votes for the House floor, told attendees at a Republican event in Texas to "watch next week, and you will see the repeal and replace of Obamacare," according to Politico.

Gary Cohn, the National Economic Council director and Trump's top economic adviser, also told CBS' "This Morning" that the AHCA should be voted on in the House this week. He said he expects it to pass.

"Do we have the votes for healthcare? I think we do," Cohn told CBS. "This is going to be a great week. We're going to get healthcare down to the floor of the House, we're convinced we've got the votes, and we're going to keep moving on with our agenda."

The AHCA hit snags the first time it was brought to the floor in March due to differences within the GOP conference.

Conservatives felt the bill did not go far enough in repealing Obamacare, while moderates were concerned over the Congressional Budget Office's estimate that 24 million more people that would go without insurance than the current system over the next decade.

Since the failure in late March, the bill has undergone changes to make it more palatable for conservatives like the House Freedom Caucus, which officially supports the new version. But recent amendments have raised concerns among moderates, and some withdrew their support of the bill.

The White House pushed for a vote on Friday or Saturday to get the plan passed during Trump's first 100 days, but House GOP leaders were unable to get enough members on board to make that happen.

As of Monday morning, the AHCA is not on McCarthy's official schedule.