Mr. Obama has been adamant that he will not link any other budget issues to the debt ceiling increase, while Congressional Republicans are demanding he compromise with them to raise the ceiling. Treasury Secretary Jacob J. Lew said Wednesday in a letter to Speaker John A. Boehner that the debt limit would be reached “no later than” Oct. 17.

While Mr. Obama’s ratings sag, he can take some solace in the standing of the Republican opposition in Congress. Nearly three-quarters of Americans disapprove of Congressional Republicans. More of the public supports Mr. Obama than Republicans to make the right decisions on the deficit, health care and the economy.

“I would blame the Republicans for a shutdown,” said Barbara Nemeth, 70, an independent in Port Richey, Fla. “It’s not their job to stalemate the government. It’s their job to work cooperatively and compromise. That has been traditionally the American democratic way. They are acting like a bunch of overgrown, spoiled brats.”

But there is little doubt that the president is being hurt by questions over his health overhaul. Only one in five Americans say they expect to be positively affected by the law.

The survey also suggests that Republicans could pay a political price going into next year’s midterm elections if there is a government shutdown. Eight in 10 Americans find it unacceptable for either the president or members of Congress to shut down the government to achieve their goals during budget negotiations. And while half the country sees Mr. Obama as working with Republicans, only one in four Americans see Congressional Republicans as working with the president to get things done.

A plurality say they would blame Congressional Republicans if a shutdown occurred.

“It’s bad on both sides,” said Gerald Muller, 86, an independent from Austin, Tex. “President Obama is not checking with experts. He’s a man who has been working alone and he’s isolated himself and now he has no one to turn to, or he won’t turn to them. He has a lot of learning to do, in my opinion. And the Republicans have their own agenda. They are kind of stubborn and don’t seem willing to compromise.”