Propelled by a torrent of blistering television advertisements, President Obama is successfully invoking Mitt Romney’s career at Bain Capital to raise questions about his commitment to the middle class, strategists in both parties say, as the candidates engage in a critical summer duel to set the terms for this fall.

Despite doubts among some Democrats about the wisdom of attacking Mr. Romney’s business career, Obama commercials painting him as a ruthless executive who pursued profits at the expense of jobs are starting to make an impact on some undecided voters, according to strategists from both sides, who differ on whether they are causing any substantial damage.

While the sense of worry and alarm that has hung over the White House for weeks is dissipating, and with his supporters relieved by the Supreme Court decision on Thursday to uphold most of his health care law, Mr. Obama faces new challenges before the conventions at the end of the summer.

People close to the Romney campaign say it could close its June fund-raising books having collected an additional $100 million, possibly more, a tally that would exceed all expectations and further extend the overall Republican financial advantage in the race.