BOSTON — Sarah Palin toured Revolutionary War sites in Boston before heading to New Hampshire on Thursday, but insisted she wasn’t trying to step on Mitt Romney’s political toes as the former Massachusetts governor formally announced his campaign for president.

Still, Palin wasn’t shy about suggesting Romney would have to work hard to persuade independent and tea party voters to support his candidacy, given his defense of Massachusetts’ near-universal health care law, which Romney signed in 2006.

The law became a model for the national health care law signed by President Barack Obama. That law is unpopular with Republican voters in general and self-described tea party voters in particular.

“He’ll have a bit more of a challenge with the independents who make up the tea party movement wanting to make sure that we’re not going to … have any excuses or perceived political reasons to grow government,” Palin said.

Romney has defended the Massachusetts law while calling for the repeal of Obama’s health care law, saying it should be up to states, not the federal government, to decide whether to expand coverage.

Palin, the GOP’s 2008 vice presidential candidate, said she agreed with giving states greater power than the federal government but still sounded a skeptical note.

“Even on a state level and a local level, mandates coming from a governing body, it’s tough for a lot of us independent Americans to accept because we have great faith in the private sector and in our own families,” she said.

Palin made her comments in response to reporters’ questions after stopping by the Bunker Hill Monument in the city’s Charlestown section, which memorializes a June 1775 battle between American colonists and British forces.

Earlier in the day, she toured the historic Old North Church and the Paul Revere House in Boston’s North End neighborhood. She also stopped by Parziale’s Bakery in the largely Italian area to order pizza and cannolis.

She shook hands with residents and fellow tourists and had her photos snapped with students and a Sarah Palin impersonator. She also offered her condolences for the victims of tornadoes that battered Massachusetts on Wednesday.

Palin has characterized her East Coast trip as an opportunity to visit some of the nation’s historic sites and not as a prelude to a presidential run.

“It truly isn’t the purpose of this trip to test the waters or to have some kind of quasi-exploratory committee or group here going on,” she said. “It’s to highlight America’s history.”

Throughout the brief visit, Palin was thronged by supporters and a few critics.

Tara Rendon, a Democrat who once worked for the late Sen. Edward Kennedy, shook hands and spoke briefly with Palin, but didn’t count herself an admirer.

“I just wish these candidates could change the tone of the conversations,” the 56-year-old Boston resident said. “President Obama isn’t doing everything right, but at least he has the right tone. He’s not inciting people.”

Donna Sirois, who was in town visiting her son, snapped pictures of Palin and said she was a big fan of Alaska’s former governor. She called Palin “a down to earth lady.”

“She’s drawing attention to people’s freedoms that are little by little being taken away from us,” said the 62-year-old Michigan resident. “Every time you turn around, you can’t do this, you can’t do that and if you do that you have to pay.”