WASHINGTON — Under mounting pressure from Donald Trump and rank-and-file Republicans, congressional leaders are talking increasingly about chiseling an early bill that dismantles President Barack Obama’s health care law and begins to supplant it with their own vision of how the nation’s $3 trillion-a-year medical system should work.

Yet even as Republicans said they will pursue their paramount 2017 goal aggressively, leaders left plenty of wiggle room Thursday about exactly what they will do. Their caution underscored persistent divisions over how to recraft a law they’ve tried erasing since its 2010 enactment, plus their desire to avoid panicking the 20 million people who’ve gained coverage under Obama’s overhaul or unsettling health insurance markets.

Sen. Johnny Isakson, R-Georgia, said Congress should put in a replacement for Obamacare that returns oversight of health care mostly to the states.

“It is unsustainable and impractical,” Isakson said in a news release. “And it’s wrong for us to say we’re going to repeal Obamacare without replacing it with a plan that we know works.”

Sen. David Perdue, R-Georgia, asked for patience with the process.

“While I am concerned with the lack of direction we’ve seen in Congress, these important decisions that will directly impact Americans’ health care must not be rushed. We have to get it right,” Perdue said in a news release. “There are various common-sense Republican health care solutions that would provide greater coverage options, drive down costs and improve continuity of care. These ideas have been studied and debated over the years, and it’s time we coalesce around a solution that will work.”

In an interview with conservative radio host Mike Gallagher, House Speaker Paul Ryan, R-Wis., said the initial repeal and replace legislation will be “the primary part of our health care policy” and would be followed by other bills. Later, he told reporters at the Capitol that while Republicans will work quickly, “We’re not holding hard deadlines, only because we want to get it right.”

Senate Majority Leader Mitch McConnell, R-Ky., said the early repeal bill would “begin to make important progress.” He said Republicans “plan to take on the replacement challenge in manageable pieces, with step-by-step reforms.” He set no timetable.

“Repealing and replacing Obamacare is a big challenge. It isn’t going to be easy,” McConnell added.

The leaders spoke a day before the House plans to give final approval to a budget that would shield the forthcoming repeal-and-replace bill from a Democratic filibuster in the Senate.

Stripping Democrats of their ability to endlessly delay that bill — a tactic that takes 60 votes to thwart — is crucial for Republicans, who have just a 52-48 edge in the Senate. That chamber approved the budget early Thursday by a near party-line 51-48 vote, drawing a Twitter thumbs-up from Trump.

“Congrats to the Senate for taking the first step to #RepealObamacare — now it’s onto the House!” the president-elect tweeted.

Trump, who enters the White House on Jan. 20, has pressed Republicans in recent days to act quickly on annulling and reshaping Obama’s law. GOP leaders seem to be taking his urgings to heart, though some have suggested his desire for speed doesn’t match Congress’ vintage lack of agility.

Asked how quickly lawmakers could send Trump a bill, No. 2 Senate Republican leader John Cornyn of Texas said, “The most important thing is when do you get 218 votes in the House and 51 votes in the Senate,” the majorities needed for passage.

“He’s not a creature of this place, so there’s always a bit of a learning curve,” said the No. 3 Senate GOP leader, John Thune of South Dakota.

Obama’s law, which he considers a trophy of his soon-to-end presidency, has provided health care subsidies and Medicaid coverage for millions who don’t get insurance at work. It has required insurers to cover certain services like family planning and people who are already ill, and curbed rates the sick and elderly can be charged.

GOP leaders hope to use their first bill to void and rewrite as much of Obama’s law as they can, but so far they’ve provided little detail. Cornyn said in a brief interview Wednesday that the early legislation will “push some of the responsibility and resources down to the states and give them more flexibility,” such as for Medicaid.

Republicans want to end the fines that enforce the statute’s requirements that many individuals buy coverage and that larger companies provide it to workers — mandates that experts say were needed to stabilize insurers’ rates. They also want to erase the taxes the law imposed on higher-income people and the health care industry, eliminate its subsidies that help people buy policies and pare back its Medicaid expansion.

But they face internal disagreements over policy, such as how to pay for their new statute and how to protect consumers and insurers during what may be a two- or three-year phase-out of Obama’s overhaul.

They also must heed Senate rules forbidding provisions that don’t directly affect taxes and spending from being safeguarded from filibusters. That means repealing important parts of the law — like the requirement that insurers offer coverage to all customers including the most ill — would have to await later bills that would need Democratic support.

Democrats have so far solidly opposed the GOP effort. But one influential conservative health care authority warned Thursday that it would be best to work with them.

“Bipartisan support for whatever is assembled is the best way, and probably the only way, to ensure that what passes in 2017 is accepted by the public” in a way Obama’s law was not, James Capretta, a fellow at the American Enterprise Institute who formerly worked for President George W. Bush, wrote Thursday in National Review Online.