He doesn’t need it and will never use it, but President Obama signed up for Obamacare anyway.

The political maneuver, announced Monday by the White House, was aimed at showing solidarity with hundreds of ­thousands of Americans enrolling in the new federal and state health-care exchanges. The move came after months of prodding from Republicans, who argued that the president should participate in his signature health-care law — although the exchanges are designed primarily for those who don’t have or can’t afford coverage.

Obama was enrolled in the D.C. exchange over the weekend, aides said, purchasing a “bronze”-level plan that will set him back about $400 a month (with a salary of $400,000, the president doesn’t qualify for subsidies). But aides said he won’t use the plan: Obama and his family will continue to receive, as all recent presidents have, medical care through the U.S. military.

As this act of political theater played out here in Hawaii, where Obama is vacationing , his administration continued to scramble back in Washington to prepare for the Jan. 1 start of coverage. Administration officials disclosed Monday that they had quietly changed the rules to allow last-minute shoppers an extra day to enroll, pushing the deadline back to midnight Tuesday.

Aides said Obama’s unique situation as president meant that he was unable to sign up for a plan online. The databases that HealthCare.gov and related sites use to verify people’s identities did not contain Obama’s personal information, aides said, so staffers had to go in person to the D.C. exchange offices over the weekend to get him enrolled.

Obama selected a bronze plan — the cheapest of four categories, below platinum, gold and silver, that designate how much of overall health-care costs are covered by an insurer.

Thus Obama is paying $5,000 a year out of pocket for a plan that a White House official said was merely “symbolic.”

The president “was pleased to participate in a plan as a show of support for these marketplaces, which are providing quality, affordable health-care options to more than a million people,” said an official who was kept anonymous in a statement issued by the White House.

For weeks, Republicans on Capitol Hill have prodded Obama to sign up for coverage under the new law and — as they view it — share in the suffering of other Americans.

Don Stewart, a spokesman for Senate Minority Leader Mitch McConnell (R-Ky.), noted that Obama “had the option to keep the plan he had, along with access to the doctors and hospitals he was comfortable with.”

Brendan Buck, a spokesman for House Speaker John A. Boehner (R-Ohio), said: “Americans are looking for a lot more than symbolic gestures. This law is a train wreck, and no one should be forced to take part in it.”

But one of the House Republicans leading the charge against the health-care law, Rep. Jason Chaffetz (Utah), said he was pleased that Obama had enrolled.

“I’m not going to take a cheap shot at him for signing up,” Chaffetz said. “It really wasn’t necessary, but if he didn’t do it, we would all bark at him. . . . He’s the president of the United States. His health care is a little different than the rest of us. We get that.”

The GOP push to get Obama to sign up dates to the crafting of the law in 2010. As the Senate neared debate on the bill that would become the Affordable Care Act, Sen. Charles E. Grassley (R-Iowa) introduced an amendment that would require Obama and Vice President Biden, as well as the Cabinet and top White House staff members, to purchase health insurance through the marketplaces.

“It’s pretty unbelievable that the president and his closest advisers remain untouched by the reforms they pushed for the rest of the country,” Grassley said at the time. “In other words, President Obama’s health-care reform won’t apply to President Obama.”

Senate Democrats rejected that approach, arguing that the purpose was to cover those not already offered insurance by their employers. Congress approved a separate provision requiring lawmakers and some of their staff members to use the exchanges, but not the president or his aides.

Nonetheless, the White House said at the time that Obama would sign up for an insurance plan through the program once the marketplaces went online.

The issue receded until earlier this month, when White House press secretary Jay Carney was asked whether Obama still planned to sign up and when. Carney confirmed that he would enroll but declined to provide a deadline.

Asked whether the news media could observe the president signing up, Carney did not offer any guarantee. “I’ll get back to you,” he said.

Obama’s enrollment, which aides characterized as an important show of support for the law, was handled with little fanfare. News photographers and reporters were not allowed to witness the president shopping for insurance plans or filling out paperwork. News that he had signed up was distributed to reporters in a one-paragraph statement attributed anonymously to a White House official.

Republican strategist Kevin Madden, a former senior adviser to 2012 presidential candidate Mitt Romney, called the move “a tactic of last resort” during the week of Christmas, when many Americans are focused on the holiday rather than the news.

“It’s not a triumphant moment,” Madden said.

Goldfarb reported from Washington.