WASHINGTON — Mocking his critics, President Barack Obama boasted Tuesday that 7.1 million people have signed up for his health care law, an unexpected comeback after a disastrous rollout sent his poll numbers plummeting and stirred fears among Democrats facing re-election this fall.

“The debate over repealing this law is over,” he declared. It’s “here to stay.”

But the late enrollment surge may do little to change the political dynamics heading into the midterm elections, particularly for Democrats running in conservative states where the health law and the president himself remain deeply unpopular. Even Obama’s advisers acknowledge that the public’s views on the law are unlikely to shift significantly between now and November.

Still, with millions of people now receiving health benefits under the law, Democrats see an opportunity to undercut Republicans still pushing to repeal “Obamacare.” And GOP lawmakers, wary of overplaying their political hand, are indeed grappling with whether to press forward with repeal or narrow their focus on replacing the law with different health measures.

In a preview of his party’s midterm messaging, Obama declared Tuesday that while the health law isn’t perfect, it is “here to stay.”

“Why are folks working so hard for people to not have health insurance? Why are they so mad about the idea of people having health insurance?” he asked a group of administration officials and supportive members of Congress in the White House Rose Garden.

Underscoring his point, Obama quoted from letters he said he had received from people helped by the law. But Republicans responded in a new round of their own quotes from people complaining about rapidly rising rates.

“The band may be playing in the White House, but hearts aren’t light for Americans struggling to afford Obamacare’s higher costs,” said a release from the Senate Republican Communications Center.

The president’s remarks amounted to a victory lap for an administration that botched the start of the long-planned enrollment period for the insurance marketplaces at the center of the landmark law. The enrollment website was riddled with technical problems, and a flurry of private policy cancellations forced Obama to recant his pledge that Americans who liked their health insurance plans could keep them.

While the Congressional Budget Office had originally estimated that 7 million people would enroll in the health exchanges this year, the CBO lowered those expectations to 6 million due to the website woes. Even inside the White House, that first estimate looked out of reach until recently.

A late wave of sign-ups pushed nationwide enrollment to 7.1 million. Still, the administration hasn’t said how many of those people have closed the deal by paying their first month’s premiums. Also unclear is how many were previously uninsured — the real test of Obama’s health care overhaul. The law also expanded coverage for low-income people through Medicaid, but only about half of the states have agreed to implement that option.

The administration hasn’t yet released an updated demographic breakdown of enrollees, such as the number of younger people whose participation is critical to the law’s success.

Politically, the law has created huge headaches for some Democrats facing re-election in November, helping to wipe away the party’s prospects for taking control of the House and putting its Senate majority in jeopardy.

Geoff Garin, a Democratic pollster, said the politics behind Obamacare will shift as more Americans feel personally invested in the overhaul — either because they’re getting care through the exchanges, staying on their parents’ plans or benefiting from patient protections.

Still, he said the law is likely to remain unpopular in states where Democrats are fighting many of their toughest races, including Louisiana, Arkansas and Alaska.  White House officials have encouraged candidates from those states to emphasize their eagerness to fix parts of the law that aren’t working rather than shy away from the measure as a whole.

One senator who appears to be following that blueprint is Mary Landrieu, a Louisiana Democrat facing a difficult re-election fight. Landrieu said of the law on Tuesday: “I continue to push to make it work even better.”

Most public polling shows the law’s opponents outnumber supporters, and nearly all surveys show it attracts few backers outside the ranks of the Democratic Party. For example, just 3 percent of Republicans and 12 percent of independents said they backed it in the latest AP-GfK poll. Democrats have also lost their advantage as the party more trusted to handle health care.

However, polling also suggests that most Americans oppose repealing the law and instead favor changes. Democratic National Committee Chairwoman Debbie Wasserman Schultz of Florida said that offers Democrats an opportunity to paint Republicans as working to deny Americans something they already have.

“Now Republicans will be trying to take those benefits away from 7 million people,” she said in an interview.

Seeking to head off that argument, some Republican leaders are encouraging want their party to focus more on replacing the health law than repealing it. Among their considerations is whether to offer a comprehensive proposal or piecemeal measures, as well as whether to keep the more popular elements of Obama’s law such as leaving children on their parents’ plans until age 26.

But the desire among Republicans to fully dismantle Obama’s signature achievement remains tempting, especially for tea party members who have significant clout in the House. Speaker John Boehner declared Monday that House Republicans will keep working to repeal the law, and he announced yet another vote this week to undo a portion.

The tea party-aligned group Americans for Prosperity announced plans Tuesday to spend more than $500,000 on television assailing Arkansas Sen. Mark Pryor, one of this year’s most vulnerable Democrats. The ad features a man lamenting how his health plan was canceled and is part of a $35 million Obamacare onslaught the group has launched since September against Democrats including Pryor, Alaska Sen. Mark Begich and North Carolina Sen. Kay Hagan.

AFP’s president, Tim Phillips, said, “We’re first and foremost holding accountable for this law the senators who voted for it.”