Undeterred by an onslaught of other events, President Obama renewed his focus on Mitt Romney’s years as a private business leader on Monday, signaling that he is not backing away from the issue of Bain Capital despite calls from other Democrats urging him to turn instead to his own future policies.

Tying his challenger’s former consulting job to the economy overall, Obama made the case that Romney’s past work — including investing in companies that specialized in shipping jobs overseas — mirrors the Republican vision for fixing the country’s economic problems.

“They believe that if we eliminate regulations and cut taxes by trillions of dollars, that the market will solve all of our problems on its own,” Obama said of Romney and other Republicans in remarks at a campaign event in a high school gymnasium here. “They argue that if we help corporations and wealthy investors maximize their profits by whatever means necessary, whether layoffs or outsourcing or whatever steps it takes, that automatically translates into jobs and prosperity for you.”

Obama’s increased attention to Romney’s Bain years comes after a report in The Washington Post detailed Bain’s investment in businesses that specialized in helping companies outsource jobs overseas. Other Democrats, including former president Bill Clinton, have worried that the strategy makes Obama seem anti-capitalist.

The president sounded somewhat attuned to the criticism Monday, telling supporters that over the past three years, he has cut taxes for the “typical working family by $3,600 and for small businesses 18 times.”

“I don’t believe every regulation is smart or that every tax dollar is spent wisely,” Obama said. “I don’t believe that we should be in the business of helping people who refuse to help themselves.”

Still, he urged voters to see this election as a choice between two different visions: Romney’s plan, which the president said would take the country back to a set of policies that he blames for the downturn, and Obama’s plan, which he said would continue investing in programs such as education, job training and health care, on which the middle class depends.

In response, Romney officials accused the president of trying to divert attention from his “abysmal economic record” with “false and discredited attacks.” “With the worst record on jobs and the economy of any president in modern history, President Obama knows he has no compelling case to make for a second term,” spokesman Ryan Williams said.

After his stop in Durham, Obama delivered a similar speech and attended two fundraisers in the Boston area, Romney’s longtime home. The Romney presence was unavoidable as one of his campaign buses, bearing Romney’s logo, circled Symphony Hall while Obama spoke there.

On Tuesday, Obama was scheduled to give an address and appear at private fundraisers in Atlanta and Miami.

Off the campaign trail, White House officials spent Monday monitoring and responding to Supreme Court rulings. Senior administration officials held a call with reporters to explain their view of the court’s decision on Arizona’s immigration law; the justices struck down several key provisions but upheld one allowing police officers to check the identification of people whom they suspect are in the country illegally.

Ahead of a ruling on the Affordable Care Act, likely to come Thursday, administration officials are getting ready to at least mitigate the political damage should the law be totally or partially thrown out. The administration has been issuing news releases praising parts of the legislation, such as its protection of patients with preexisting conditions and its requirement that parents be allowed to keep their children on their insurance policies until age 26.

On Monday, the White House put out another such statement, this one saying that more than 5.2 million Medicare recipients are saving $3.7 billion on prescription drugs as a result of the Affordable Care Act.

Whether the court upholds, tosses or partially rejects the law could define the tenor of the rest of the presidential campaign.

On his two-day campaign swing, the president will collect upward of $5.5 million, according to an Obama campaign official — money that will go into the Obama Victory Fund, a joint fundraising committee of Obama for America, the Democratic National Committee and several state Democratic parties.

The trip includes a $35,800-per-couple fundraising dinner at a private residence in Weston, Mass., two $40,000-per-person receptions in Boston and Miami, and a $35,000-per-ticket event in Atlanta. Three larger-crowd, smaller-dollar events will include a reception at the Fillmore at the Jackie Gleason Theater in Miami, where entertainer Marc Anthony will perform.

The Boston trip included Obama’s 100th fundraiser this year, according to Mark Knoller of CBS News, who keeps a variety of presidential statistics.