WASHINGTON — When President Obama dropped in to give a pep talk to workers at the American Red Cross here on Tuesday afternoon, it seemed like a standard ritual for a leader confronting a natural disaster. But in the final week of a presidential campaign that has been scrambled by an epic storm, nothing can be divorced from politics.

Mr. Obama, eager to project the image of a president responding forcefully to the crisis, promised the storm’s victims in New Jersey, New York and elsewhere that federal help was on the way. And he warned the rank and file in federal agencies that they had better not get in the way of that effort.

“My message to the federal government: no bureaucracy, no red tape,” said Mr. Obama, flanked by Red Cross employees. “Get resources where they’re needed as fast as possible.” Referring to a call he held earlier with 20 governors and mayors, Mr. Obama said he told them, “If they’re getting ‘no’ for an answer somewhere in the federal government, they can call me personally at the White House.”

For a president locked in a razor-thin battle for re-election, the storm has presented a moment — both promising and perilous — to rise above the partisan fray and shift the tone of a campaign that had settled into a grinding slog to Election Day.