(CNN) Two sources close to the health care legislative process tell CNN the White House is exploring whether to take one more stab at repealing and replacing Obamacare before President Donald Trump hits the key milestone of 100 days in office late next week.

The renewed effort comes as Congress returns from recess next week and as the Trump administration is fielding questions about its legislative accomplishments during its first 100 days in office.

"I don't think it's impossible to think we'll have a vote," a senior administration official said optimistically. But the official cautioned that some GOP House members are still at odds over some of the bill's sticking points.

"I don't think it's having to rewrite the bill. It's just a total trust gap. As soon as we solve that, we can have a vote," the official said.

Trump himself was confident about the chances of Congress passing a health bill Tuesday in Wisconsin, telling CNN affiliate WTMJ : "We are going to have a big win soon, because we are going to have health care and that's gonna happen. And there was no lose with health care, this is just a constant negotiation and the plan is getting better and better all the time."

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And Vice President Mike Pence told CNN aboard the USS Ronald Reagan that Trump is "determined to keep our promise" on health care. "I'm very confident that in the days ahead, we're going to see the Congress come together and we're going to take that important first step to repeal and replace Obamacare with the kind of health care plan President Trump has envisioned," he told CNN's Dana Bash in an exclusive interview Wednesday.

Against the clock

But the White House's timeline may be too optimistic, another source said.

"We'd all like to have it done by then, but not sure that's feasible," another GOP source close to the process said. Speaking of the White House, the source added: "I think they have that in mind. But we need to manage expectations. We've learned a lesson on arbitrary deadlines."

The White House and House Republicans pulled legislation to repeal and replace Obamacare last month after failing to garner enough support for passage.

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That GOP source said members continue to discuss ways to tally up the 216 votes needed to pass an Obamacare repeal measure through the House. But Congress has a more pressing concern as members return to Capitol Hill -- approving a continuing resolution to avoid a government shutdown and keep the government running.

"The No. 1 priority is government funding when we return," the source said.

The prospect of the government shutting down around the 100-day milestone is not lost on White House and congressional officials. Funding for most departments and agencies of the federal government runs out on April 28.

"That would be a disaster," a key GOP congressional source said.

The sticking points

On the Hill, the conversations that matter are between House Freedom Caucus Chairman Mark Meadows and Tuesday Group co-chairman Tom MacArthur. They have been speaking continuously throughout the recess and touching base with Pence's office and House leadership.

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The focus has remained on the outstanding issues that have always been there: Meadows and his members want to get at as many of the Affordable Care Act's Title One regulations as possible. MacArthur and the conference's moderates want to ensure any move in that direction doesn't gut the elements of Obamacare they campaigned to keep. The talks have continued to focus on three areas identified before the congressional recess: essential health benefits, community rating and guaranteed issue. The work has centered on what the triggers would be for states to opt out of those regulations and how much money could be added to the bill to address concerns that the regulations would essentially undercut the existing ban on insurers discriminating on the basis of pre-existing conditions.

The reality remains, according to one person involved, that the continued push to find an amenable compromise on the Title One changes requested by the Freedom Caucus is still a very difficult sell to the broader conference.

As of now, the rank-and-file haven't been given any information on what has been discussed, and there has been no finalized language presented to anyone involved. The White House has made clear to those involved on Capitol Hill that they would be very interested in having a vote as soon as next week.

Senior Capitol Hill aides remain very skeptical.

"Longshot at best," one GOP aide said. "But the White House clearly wants it."