White House officials were quick to tell CNN that Short had gotten ahead of White House deliberations.
McConnell explained to Trump that senators are open to tackling specific aspects of health care - namely, trying to lower prescription drug prices. "The Republican Party will be known as the Party of Great HealtCare [sic]". "They came up with Obamacare and it is bad". However, McConnell said that during a conversation with Trump on Monday, the senator "made it clear to him" that the Senate was "not going to be doing that".
On Capitol Hill, Republicans were relieved.
The No. 2 Senate Republican, John Thune of South Dakota, said the president "has some big ideas and, to his credit, wants to solve problems".
But Thune said, "you run into that wall of reality", of a divided Congress with Democrats in control of the House, which requires bipartisanship.
"I don't like the way the votes are being tallied", Trump said.
When asked whether the two Senate committees overseeing health-care policy are planning to draft a replacement proposal for the Affordable Care Act, Grassley responded flatly: "No".
At the time, President Trump echoed McConnell's more measured tone after years of Republican attacks on Obamacare.
Though parts of the Affordable Care Act are unpopular with voters, some of its key reforms such as protections for patients with pre-existing conditions have been nearly unanimously embraced.
Trump accuses Democrats of seeking "a socialist takeover of American healthcare", and is certain to take that argument onto the 2020 campaign trail.
Senate Minority Leader Chuck Schumer said Trump will "hold Americans hostage through 2020" on an issue that affects millions of people.
House Speaker Nancy Pelosi of California said Democrats' health care battle with Trump is "a values fight".
Trump's statements come a week after his administration announced that it now agreed with a judge's ruling that the entire Affordable Care Act should be scrapped.
In his tweets, Trump claimed that a bill is in the works.
Sen. Michael Bennet, D-Colo., said Trump has failed to deliver on a promise for quality, affordable health care for everybody.
Aides say all 197 Republicans are expected to sign.
It soon became clear, however, that other Republicans had little appetite to take on an issue that benefited Democrats during last year's midterm elections. A Quinnipiac University poll last week found 55% of Americans supporting the improvement and not the replacement of the nation's health care system.
Even with GOP control of both chambers of Congress prior to that, Republicans were unable to agree on a plan to replace the ACA - something McConnell noted on Tuesday.