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 redraft 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.

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 next Friday, 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.