Congress may have to choose next week between keeping the government open and voting to repeal Obamacare — but President Donald Trump thinks it can do both.

"We have a good chance of getting (health-care legislation passed) soon. I'd like to say next week, but I believe we will get it and whether it's next week or shortly thereafter," Trump said during a Thursday joint news conference with Italian Prime Minister Paolo Gentiloni. "As far as keeping the government open, I think we want to keep the government open, don't you agree? So, yeah, I think we'll get both."

Congress returns from recess next week, with only days before the current resolution funding the government expires on April 28. Ahead of the scramble to keep the government running, reports Thursday indicated that the White House may push for a vote on a revised plan to replace the Affordable Care Act when Congress comes back.

Tackling both complex issues in one week would likely prove a daunting task.

There is not yet legislative text for the revised health-care proposal, and no vote is scheduled for next week, so far, three GOP aides told CNBC. It is unclear if this health-care plan could garner the votes needed to clear the House or the Senate.

A Republican congressional representative who spoke to CNBC expects Congress to avoid a government shutdown next week. CNBC previously reported that Republicans, who hold majorities in both chambers of Congress, would be willing to adopt a temporary measure keeping the government running for about another week while lawmakers continue budget negotiations.

An attempt to replace the ACA failed in dramatic fashion last month as House Republicans struggled to balance the concerns of conservative and moderate members of their caucus. Trump and House leaders initially signaled they would move to a tax reform bill, but eventually started to seek tweaks to push a heath-care plan through before pursuing a tax overhaul.

"The plan gets better and better and better and it's gotten really, really good," Trump said Thursday.

Trump contended that Republicans never gave up on pursuing health-care legislation. After the bill failed last month, Trump told reporters, "I would say that we will probably start going very, very strongly for the big tax cuts and tax reform."

— CNBC's John Harwood and Kayla Tausche contributed to this report.

Watch: Highlights of press conference with Trump and Italian PM