Senate Majority Leader Mitch McConnell

Updated on Aug. 10 at 4 p.m. ET

President Trump is continuing to voice his frustration with Senate Majority Leader Mitch McConnell, tweeting on Thursday that the Kentucky Republican should "get back to work" after last month's failure to pass a health care alternative to the Affordable Care Act.

The president's latest tweets calling out the Kentucky Republican came as Trump himself is taking a "working vacation" at his own golf resort in New Jersey.

The White House says the fight over health care is not over, but on Capitol Hill, Republicans are ready to move on.

"The president isn't giving up on health care and neither should the Senate," Office of Management and Budget Director Mick Mulvaney declared on CNN on Wednesday.

On the Senate floor that same morning, Senate Majority Leader Mitch McConnell, of Kentucky, was already focused elsewhere.

Senate Republicans don't appear to be too worried about President Trump's latest round of threats.

The Senate voted Tuesday to begin debating a replacement for the Affordable Care Act. It remains uncertain as to what that replacement might look like. No formal legislation has been drafted. But senators moved to take the procedural first step, known as a "motion to proceed." The vote was 51-50, with Vice President Pence casting the tiebreaking vote.

Debate will now begin, most likely on a measure to fully repeal the law, also known as Obamacare.

The Republican scramble to repeal and replace the Affordable Care Act has yielded yet another version of a health care overhaul bill, along with yet another score from the Congressional Budget Office — the second analysis from the nonpartisan agency in two days.