DES MOINES, Iowa — In a presidential race seemingly frozen in place for months, the advantage has shifted toward President Barack Obama after a series of miscues by Mitt Romney, punctuated by the Republican challenger’s comments about people who pay no income tax.

Despite a continuing gray economic sky and unrest in the Mideast, the president has edged ahead of Romney in polls in some of the most competitive states, including Iowa and Virginia, and forced Romney to redouble efforts in Florida and Ohio, without which he has little chance of becoming president.

With about six weeks left before Election Day and early voting under way in some states, Romney faces a problematic map, a ticking clock and a campaign demeanor that has failed to click with many voters.

Obama’s momentum did not come overnight. It built over several weeks in which Romney hit some potholes while the president made few errors and benefited from previously unseen advantages in advertising strategy and fundraising.

Weeks of campaigning remain, and the three debates, starting Oct. 3, are the kind of events that could change the momentum again. But the race has bent toward Obama at a pivotal moment, according to public and internal campaign polls as well as interviews with leading Democratic and Republican strategists in the most closely contested states.

“Months of paid media about Romney not caring about people, being out of touch ... it came into complete focus with Romney making the case against himself,” Democratic strategist Tad Devine, a top aide to past Democratic nominees Al Gore and John Kerry, said about a video that surfaced last week of Romney speaking at a private fundraiser in May.