The CNN/Opinion Research survey, conducted Saturday and Sunday, is one of the first released after Friday's last-minute compromise between House Republicans, Senate Democrats and the White House.
It found that 58% of Americans approve of the compromise, while 38% disapprove and 5% had no opinion. That includes two-thirds of all Democrats and 56% of independents. But Republicans were split on the deal, with 47% approving and 49% disapproving.
Forty-eight percent of respondents say President Obama and congressional Democrats are more responsible for the agreement, while 35% credit Republicans and 11% say they share equally. Obama personally gets good marks for his handling of the negotiations — 54% approve, while only 44% approved of how the respective party leaders in Congress handled them.
On some of the most contentious issues that held up an agreement, voters tended to side with Democrats. Only a third of voters support eliminating federal funding for Planned Parenthood. Even fewer — 28% — favored legislation to prevent the Environmental Protection Agency from spending money to enforce greenhouse gas regulations. About four-in-10 respondents support blocking funds for the implementation of Obama's healthcare law.
Though a shutdown never came to be, 24% say they would have viewed one as a crisis, and 39% said it would have been a major problem. So-called "tea party" supporters were the least likely to say a shutdown would have been a problem — 22% say it would not have been a problem at all, and 32% say it would have been only a minor problem.
The budget debate appears to have taken a small toll on Obama's overall popularity, though. His approval rating dropped from 51% in March to 48% in the new survey, a result that is within the margin of error. House Speaker John Boehner (R-Ohio) has an approval rating of 41%, while 44% disapprove.