WASHINGTON — Republican anxiety is mounting over voting to unravel the health care law without having an alternative in hand, fanned by words of encouragement from Donald Trump to a GOP senator who wants to simultaneously repeal and replace the statute.

GOP leaders have made dismantling President Barack Obama’s treasured health care overhaul their premier 2017 priority. But even as the Republican-run Senate moves toward passing a budget that would make it harder for Democrats to protect Obama’s law later, at least six GOP senators have expressed qualms about repeal without having a substitute — something Republicans have failed for years to produce.

“We should start immediately to repeal, reform and replace Obamacare, and it shouldn’t be finally repealed until we have a replacement ready,” Senate Health Committee Chairman Lamar Alexander, R-Tenn., whose panel will be at the center of this year’s battle, said in a brief interview.

Sen. Rand Paul, R-Ky., who wants repeal and replace together, said the president-elect telephoned him Friday to voice support for that timing. Trump voiced that opinion shortly after his November election, but he called Paul as GOP congressional leaders have moved in a different direction: A quick repeal vote, followed by work on an alternative that could take months or years to craft.

“He’s aware of my arguments for doing replacement at the same time, and he agreed,” Paul said.

Even if Congress passed repeal rapidly, Republicans say they would phase it in, perhaps over two or three years.

Republicans don’t want to abruptly end coverage for 20 million Americans who’ve received coverage under the 2010 law, and don’t want to be vulnerable to Democrats already accusing them of preparing to tear down the statute without knowing how or if they’ll replace it.

“Turn back before it’s too late,” Senate Minority Leader Chuck Schumer, D-N.Y., said on the Senate floor just short of midnight as Democrats, before leaving for the night, lambasted Republicans with five-and-a-half hours of speeches. “It will damage your party,” Schumer said, “and it will hurt millions of Americans, far more importantly.”

Highlighting GOP indecision, Steve Bannon, who will be White House senior adviser after Trump is sworn in Jan. 20, said, “We’re still thinking that through” when asked by reporters after a meeting in the Capitol if repeal and replace should happen together.

The Affordable Care Act, signed into law in 2010, has required people to obtain coverage. It also created subsidies to help lower-earning people buy policies and expanded Medicaid, but the overhaul has been troubled by rising costs for many consumers and markets that some insurers abandoned.

The burgeoning Republican divisions come as the GOP-led Senate pushed toward a final vote this week on a budget that would prevent Democrats from using a filibuster to block a later repealing Obama’s overhaul. That’s crucial because filibusters take 60 votes to halt in a chamber that Republicans control by only a 52-48 margin.

Others voicing Paul’s sentiment include Republican Sens. Susan Collins of Maine, Ron Johnson of Wisconsin, Tom Cotton of Arkansas and Bob Corker of Tennessee.

The budget gives congressional committees until Jan. 27 to produce legislation annulling much of the health care law, although consequences for missing that deadline are minor.

Even so, Corker, Collins and three other GOP senators introduced a budget amendment delaying that target date until March 3. Corker said that would provide “additional time to get the policy right.”

On CBS’ “Face the Nation” on Sunday, Senate Majority Leader Mitch McConnell, R-Ky., said replacement legislation would follow repeal “rapidly” but did not define the timetable.

Besides health care, senators are focused this week on confirmation hearings for Trump’s Cabinet picks.

In Tuesday’s initial hearings, committees were examining Sen. Jeff Sessions, R-Ala., Trump’s selection for attorney general, and retired Marine Gen. John Kelly, his choice for homeland security secretary. Seven others were set for hearings this week.

Also Tuesday, a Senate Intelligence Committee hearing was set to explore spy agencies’ conclusion that Russia meddled in the U.S. election by hacking and distributing Democratic party emails to help Trump win the White House.

House Speaker Paul Ryan, R-Wis., met in his office Monday with top Trump transition aides to discuss GOP plans to revamp the tax system.

“I need to make sure that we are all on the same page. We have a huge challenge here, it was better tonight,” incoming White House chief of staff Reince Priebus was heard saying after the two-hour meeting.

Democrats’ Senate talk-a-thon condemning the GOP health care push ended just after midnight after roughly two dozen lawmakers spoke to C-SPAN cameras on the nearly vacant Senate floor. Democrats said Republicans want to “make America sick again” and were using a “repeal and run” strategy.