PHILADELPHIA — President Obama challenged wavering members of his party on Monday not to give in to political fears about supporting health care legislation, asserting that the urgency of getting a bill through Congress should trump any concern about the consequences for Democrats in November.

In a high-octane appearance that harked back to his “yes we can” campaign days, Mr. Obama jettisoned the professorial demeanor that has cloaked many of his public pronouncements on the issue, instead making an emotional pitch for public support as he tries to push the legislation through a final series of votes in Congress in the next several weeks.

With the fate of his signature initiative on the line, and Republicans eager to portray Democrats as out of step with the country and incapable of governing, Mr. Obama seemed to relish the opportunity to cut loose and make his case on his terms, as he often has at pivotal moments.

And, with his back to the wall, the president appeared intent on reassuring his party that he was as confident as ever in his powers to explain, persuade and capture the politics of the moment.