The poll finds Americans are pessimistic about the prospects for Mideast peace and do not think the United States should involve itself in the fighting between Israel and Hezbollah.
More than 60 percent think the conflict will lead to a larger war in the region, and a similar number doubt Israel and the Arab states will ever be able to live in peace.
Just 32 percent said U.S. troops should be sent to the Mideast as part of a United Nations peacekeeping force, although 60 percent favor such a force.
More Americans (47 percent) said they approve of how Mr. Bush has handled the conflict so far than disapprove (27 percent), but one in four said it's too early to form an opinion.
Mr. Bush's overall approval rating remains low — and in an additional diplomatic concern, most Americans (60 percent) now think he is not respected by foreign leaders.
That number is down significantly since just before the Iraq war began in 2003, when about half of Americans thought Mr. Bush was respected around the world.
Slightly more than half of Americans said they believe Mr. Bush respects foreign leaders, a number that's also down from 2003.
Most Americans do not think the United States should step up its diplomatic efforts in the latest Mideast crisis. Fifty-eight percent said solving conflicts between Israel and Mideast nations is not America's responsibility, while 33 percent said it is.
By 59 percent to 31 percent, Americans said the United Nations and other countries, rather than the United States, should take the lead in solving international crises.
Pessimism about the Mideast extends to U.S. efforts in Iraq. Just 27 percent of Americans — the lowest number to date — now believe the United States is winning the war, compared with 13 percent who say the Iraqi resistance is winning and 58 percent who call it a stalemate.
Fifty-seven percent of Americans said the war was going badly, including 27 percent who said it's going very badly.
While a majority of Americans, 58 percent, still believe success in Iraq is at least somewhat likely, 53 percent think Iraq will never become a stable democracy, up 10 points from last month.
Forty-one percent said the U.S. presence in Iraq is making the region less stable, nearly double the number in March. Twenty-five percent said the U.S. presence in Iraq was making the region more stable.
Sixty-nine percent also said the U.S. presence in Iraq is hindering U.S. diplomatic efforts elsewhere in the Mideast. Nearly three in four said the war in Iraq has worsened America's image in the world.
Blame for the current Mideast crisis was split, with about half of those polled saying Israel's response in the conflict was about right, and a similar number saying both Israel and Hezbollah were at fault.
A separate CBS News/New York Times poll on Congress and the 2006 election (.pdf) found continued low approval ratings for lawmakers and the president translating into a Democratic lead in the midterm voting this fall.
If the midterm elections for the House of Representatives were held today, 45 percent of registered voters said they would support the Democratic candidate, while 35 percent would support the Republican.