“There’s now a new story line: he’s determined, disciplined, decisive and effective,” Mr. Podesta said. “He’s got a much stronger hand” for controlling the pace of American withdrawal from Afghanistan.

But attention will soon shift from the daring commando raid to the partisan fight over reducing the deficit and raising the federal debt limit. There is no impact on conservative resistance to tax increases, noted the longtime Republican budget expert Steve Bell; Democrats have made tax increases a condition for cuts in Medicare and Social Security.

While it lasts, however, Mr. Obama’s higher standing among independent voters could pressure Republicans to compromise on lower-profile issues that do not fall into well-worn partisan grooves.

Those issues include education, corporate tax overhaul and immigration, which Mr. Obama is to address in a speech this week. Advisers say he will repeat his call for a comprehensive new policy.