By Lauren Fox, MJ Lee, Dana Bash and Deirdre Walsh, CNN

(CNN) -- The Senate will not vote on the Graham-Cassidy bill to repeal Obamacare, Republican leaders announced Tuesday.

The decision is another blow to President Donald Trump's attempts to repeal Obamacare, a long-time Republican campaign promise and a centerpiece of his legislative agenda. Trump is now also floating the idea of working with Democrats on changes to the health care law, repeating his budget deal he reached earlier this month.

Majority Leader Mitch McConnell met with lawmakers Tuesday to take stock of where his members are on the proposal and make the call once and for all if Graham-Cassidy, the latest bill to repeal and replace Obamacare, will get a vote in the Senate. The decision was that the votes simply weren't there.

On Monday, Sen. Susan Collins, a Republican from Maine, finally came out against the bill, a position she'd been teetering toward for days. Sens. John McCain of Arizona and Rand Paul of Kentucky also opposed to the measure.

The calculations for health care are agonizing for McConnell. Putting a controversial bill on the floor without the votes exposes 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.

South Carolina Sen. Lindsey Graham, a bill sponsor, publicly thanked McConnell. "Thank you, it's complicated, it's difficult politics," Graham told reporters.

McConnell "didn't try to explain the decision" during the lunch, Sen. Tim Scott said. "It's obvious -- we don't have the votes right now, you don't vote until you have them."

Can it stay alive via tax bill?

While the repeal effort has risen from the dead before -- several times -- most in the chamber were resigned that this time would be was unlikely to get a hold of phoenix-like properties before the September 30 deadline to move the bill with 50 votes to beat a Democratic filibuster.

Regardless of what happens to Graham-Cassidy, there are signs that plenty of Republicans in Washington -- both in the White House and Capitol Hill -- are simply not ready to give up.

President Donald 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 are rumblings among lawmakers about ways to keep trying on repeal if this week ends with defeat (the current legislative vehicle that Republicans are using to move a health care bill without any Democratic support expires after Saturday).

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."

Working with Democrats?

At a White House meeting with both Democratic and GOP lawmakers, the President warned Republicans in bipartisan meeting he'd 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, 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

Rep. Richard Neal, D-Massachusetts, ranking member on the Ways and Means Committee said "Clearly," he said when asked if the President made the 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.

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