WASHINGTON — Republicans held together and shoved their signature tax overhaul a crucial step ahead Tuesday as wavering GOP senators showed a growing openness. But its fate remained uncertain, and a planned White House summit aimed at averting a government shutdown was derailed when President Donald Trump savaged top Democrats and declared on Twitter, "I don't see a deal!"

"It's time to stop tweeting and start leading," Senate Minority Leader Chuck Schumer retorted after he and House Minority Leader Nancy Pelosi rebuffed the budget meeting with Trump and top Republicans.

Trump lunched with GOP senators at the Capitol and declared it a "love fest," as he had his previous closed-doors visit. But the day underscored the party's yearlong problem of unifying behind key legislation — even a bill slashing corporate taxes and cutting personal taxes that's a paramount party goal.

Tuesday's developments also emphasized the leverage Democrats have as Congress faces a deadline a week from Friday for passing legislation to keep federal agencies open while leaders seek a longer-term budget deal. Republicans lack the votes to pass the short-term legislation without Democratic support.

In a party-line 12-11 vote, the Senate Budget Committee managed to advance the tax measure to the full Senate as a pair of wavering Republicans — Wisconsin's Ron Johnson and Tennessee's Bob Corker — fell into line, at least for the moment. In more good news for the GOP, moderate Sen. Susan Collins of Maine said it was a "fair assumption" that she was likelier to support the bill after saying Trump agreed to make property taxes up to $10,000 deductible instead of eliminating that break entirely.

But the fate of the legislation remained uncertain as it headed toward debate by the full Senate, which Republicans control by a slender 52-48. GOP leaders can afford just two defectors, and a half dozen or more in their party have been uncommitted. They include some wanting bigger tax breaks for many businesses but others cringing over the $1.4 trillion — or more — that the measure is projected to add to budget deficits over the next decade.

"It's a challenging exercise," conceded Senate Majority Leader Mitch McConnell of Kentucky. He compared it to "sitting there with a Rubik's Cube and trying to get to 50" votes, a tie that Vice President Mike Pence would break.

Corker, who's all but broken with Trump over the president's behavior in office, is among a handful of Republicans uneasy over the mountains of red ink the tax measure is expected to produce. He said he was encouraged by discussions with the White House and party leaders to include a mechanism — details still unknown — to automatically trigger tax increases if specified, annual economic growth targets aren't met.

"I think we're getting to a very good place on the deficit issue," Corker said.

But other Republicans are wary of backing legislation that would hold the hammer of potential future tax increases over voters' heads.

"I am not going to vote to automatically implement tax increases on the American people. If I do that, consider me drunk," said Sen. John Kennedy of Louisiana.

Collins said she'd also won agreement that before completing the tax measure, Congress would approve legislation restoring federal payments to health insurers that Trump scuttled last month. That bill has had bipartisan support, but it's unclear if Democrats would back it amid partisan battling over the tax bill.

McConnell and House Speaker Paul Ryan, R-Wis., met with Trump at the White House despite the top Democrats' no-shows. Trump highlighted their absence by appearing before reporters flanked by two empty chairs bearing Schumer's and Pelosi's names.

Trump said Democrats would be to blame for any shutdown, despite GOP domination of government.