WASHINGTON -- Support for President Barack Obama's health-care effort has declined over the past five weeks, particularly among those who already have insurance, a Wall Street Journal/NBC News poll found, amid prolonged debate over costs and quality of care.

In mid-June, respondents were evenly divided when asked whether they thought Mr. Obama's health plan was a good or bad idea. In the new poll, conducted July 24-27, 42% called it a bad idea while 36% said it was a good idea.

Among...