WASHINGTON (CNN) -- A majority of the U.S. public disapproves of President Bush's decision to veto a war spending bill that called for U.S. troops to leave Iraq in 2008, according to a CNN poll released Tuesday.

The poll found that 54 percent of Americans opposed Bush's May 1 veto, while 44 percent backed the president's decision to kill the $124 billion bill.

Now that the veto has been cast, 57 percent of Americans said they want Congress to send another spending bill with a timetable for withdrawal back to the White House, the poll found -- but 61 percent would support a new bill that dropped the timetables in favor of benchmarks for the Iraqi government to meet to maintain American support. (Full results [PDF])

While it found that more Americans believe Congress, rather than the president, should be responsible for setting policy in Iraq, the survey may give the Democratic leadership some pause. The percentage of people saying Democratic control of Congress is good for the country dropped from 59 percent in a March poll to 51 percent now.

The poll, conducted by Opinion Research Corp. for CNN, surveyed 1,028 American adults between Friday and Sunday. It has a sampling error of 3 percentage points.