Majority Leader Mitch McConnell announced the decision at a lunch with fellow Republicans on Capitol Hill, conceding what had become clear Monday night: They didn't have the votes.
"We haven't given up on changing the American health care system. We are not going to be able to do that this week," McConnell told reporters Tuesday. "But it still lies ahead of us, and we haven't given up on that."
Even as McConnell and his colleagues vowed that their goal of overhauling the country's health care system was far from over, Tuesday marked a clear end to the latest campaign to try to jam through a partisan bill to gut the Affordable Care Act. The budget vehicle Republicans were using to move the bill forward without any Democratic support was set to expire at the end of this week.
The sponsors of Graham-Cassidy said they were disappointed but would try again -- next time through a more transparent process. The new plan, they said, is to take another crack at health care through the 2019 budget reconciliation process (which would again only require 50 votes for passage) and hold committee hearings, markups and reach out to Democrats.
The political calculation leading up to Tuesday was agonizing for McConnell. Putting a controversial bill on the floor without the votes would have exposed members to political fallout and attack ads. Many Republicans hadn't even taken a public position on Graham-Cassidy, a bill that the Congressional Budget Office said Monday
would drastically cut Medicaid and lead to millions of people not having health insurance compared to the status quo.
In the end, three Republicans had publicly opposed the bill: Sens. John McCain, Susan Collins and Rand Paul.
McConnell "didn't try to explain the decision" during the lunch, GOP Sen. Tim Scott said. "It's obvious -- we don't have the votes right now, you don't vote until you have them."
Working with Democrats?
At a bipartisan White House meeting, the President warned Republicans Tuesday that he would work with Democrats on health care if they fail to act.
Trump mentioned how much he liked the deal he negotiated recently with Senate Minority Leader Chuck Schumer and House Minority Leader Pelosi on raising the debt ceiling and government spending, according to a source familiar with the discussion and with Democratic lawmakers.
Democratic Rep. Linda Sanchez told reporters that Trump told the group he was "disappointed" in those Republican senators who came out against the Senate bill. She said he "chided" the GOP members there that he could end up working with Democrats on health care legislation
Democratic Rep. Richard Neal, ranking member on the Ways and Means Committee, said "clearly" when asked if the President was making a threat.
"He made that clear that if he didn't get what he wanted, he was going to work with Democrats on a plan," Neal told reporters.
Graham, however, brushed off the suggestion that Trump might once again catch Republicans off-guard by striking a deal with Democrats. "I think the President is not going to do anything that doesn't repeal and replace Obamacare in a substantial way -- don't sell him short," he told CNN.
Will Republicans really move on?
What's not clear is whether Republican lawmakers will truly move on from Obamacare repeal for the time being -- or attempt to find another way to try again.
Before McConnell's announcement, there were signs that plenty of Republicans in Washington were simply not ready to give up.
Trump said Tuesday that he was "disappointed" in several senators, in an apparent reference to McCain, Paul and Collins.
"At some point there will be a repeal and replace but we'll see whether or not that point is now or whether it will be shortly thereafter," Trump said. "But we are disappointed in certain so-called Republicans."
On Capitol Hill, there were rumblings among lawmakers about ways to keep trying on repeal if this week ends with defeat.
One idea -- which hardly enjoys widespread support at the moment -- is to tie both health care and tax reform to the 2018 budget.
Graham and Sen. Ron Johnson, who both sit on the budget committee, have advocated for this idea. It has raised concerns among Republican lawmakers and staff alike who know just how messy that could potentially be.
One GOP aide bluntly described that scenario as "a nightmare."
This story has been updated.