WASHINGTON >> A substantial 12 million people have enrolled for coverage this year under the very health care statute that President Donald Trump and the Republican Congress want to erase, the government said today.

With a crunch-time House vote on a GOP bill replacing that law planned for next week, Vice President Mike Pence ensured conservative lawmakers that the administration was open to changes.

Pence’s trip to the Capitol, and an evening all-hands meeting of House Republicans to count votes, came as GOP leaders strained to win backing for besieged legislation that’s uniformly opposed by Democrats. The bill would strike down much of former President Barack Obama’s 2010 overhaul and reduce the federal role, including financing, for the nation’s health care consumers.

“Where is the sweet spot, that’s what we’re working on,” said Rep. Barry Loudermilk, R-Ga., among the conservatives who met with Pence. He said the vice president’s pitch was: “The process is open, we’re still working on it, bring your ideas forward and let’s get a bill done.”

With opposition from conservative and moderate GOP lawmakers endangering the measure in the House and Senate, President Donald Trump was expected to urge lawmakers to back the bill in remarks in Nashville, Tennessee. Health secretary Tom Price was using phone calls to lobby Republican governors, some of whom — with home-state GOP members of Congress — oppose the bill’s phaseout of Obama’s expansion of Medicaid to 11 million additional lower-income Americans.

Underscoring GOP leaders’ push-and-pull problem, around 60 conservatives who met with Pence proposed revisions in the other direction, including a hastening of the Medicaid expansion phaseout to 2018 instead of the legislation’s 2020.

“He gave us a lot of hope,” said Rep. Mark Walker, R-N.C., leader of the group that met with Pence.

The White House, GOP leaders and rank-and-file lawmakers were negotiating over modifications that could be made when the bill reaches the House floor. On CNN, House Speaker Paul Ryan, R-Wis., said changes might give states more “flexibility” to oversee Medicaid.

In the Senate, the GOP’s 52-48 edge and widespread dissension leaves leaders little leeway. Sen. Charles Grassley, R-Iowa, expressed worries about higher costs on seniors and predicted the Senate would reject the bill without changes.

Conservatives want deeper cuts in the overall Medicaid program than the Republican bill plans and a work requirement for able-bodied constituents. They’re also seeking less generous tax credits for people’s health care costs and elimination of Obama’s insurance requirements, including mandatory coverage of specified services like drug counseling.

Every one of those proposals would endanger support from moderates.

“This is going to take a lot of political capital from the president” and congressional leaders, said Rep. Dennis Ross, R-Fla.

The bill would enfeeble Obama’s individual mandate — the requirement that Americans buy coverage — by abolishing the tax fine on violators. It would end subsidies that help low-income people with high insurance premiums the most and replace them with tax credits that are bigger for older people. It would cut Medicaid, repeal the law’s tax increases on higher earning Americans and allow 30 percent higher premiums for consumers who let coverage lapse.

The latest government sign-up numbers missed Obama’s target of 13.8 million people for 2017. The figures represent initial enrollment, and there’s usually significant attrition over the course of a year.

Nonetheless, experts said the report undercuts Republican claims that the health law’s insurance markets are teetering toward collapse, which they say makes repealing the law crucial.

“While there’s a big debate in Washington about the future of the Affordable Care Act, the law remains in place for now and is covering millions of people,” said the nonpartisan Kaiser Family Foundation’s Larry Levitt, using the formal name of Obama’s statute.

The official national figure of 12.2 million excludes 765,000 people signed up under a related Obama-era law used by New York and Minnesota.

The Centers for Medicare and Medicaid Services released the figures a day before the House Budget Committee plans to advance the GOP bill in a potentially tight vote. The committee can’t make significant changes, but Republicans were expected to approve non-binding suggestions to nail down votes.

GOP support became scarcer when the nonpartisan Congressional Budget Office found this week that the legislation would push 24 million Americans off coverage in a decade and shift out-of-pocket costs toward lower income, older people. That’s 4 million more than the 20 million who’ve gained either Medicaid or insurance coverage under Obama’s law.

Hundreds of conservative activists rallied outside the Capitol in sub-freezing weather to call on congressional leaders and Trump to abandon the GOP bill and fully repeal Obama’s law. The rally was organized by FreedomWorks, a conservative group backed by the billionaire Koch brothers.

“They’re telling us that you campaigned for Obamacare light and you want partial repeal!” said Sen. Rand Paul, R-Ky., among conservative lawmakers who say the House GOP bill is too timid.

“No!” the crowd replied.

Nevada GOP Gov. Brian Sandoval, who expanded Medicaid coverage to over 300,000 additional people in his state, said in a phone call, Price promised “flexibility” in administering the program.

Associated Press writers Erica Werner in Washington, David Pitt in Des Moines, Iowa and Alison Noon in Carson City, Nevada, contributed to this report.