No less than 51% of Americans were against Bush's request for an additional $87 billion to fund operations in Iraq and Afghanistan, the poll conducted by Newsweek said.
Only 42% of those polled said they favour the additional spending.
But 55% of the respondents said the Bush administration did a poor job in preparing the citizens for the cost increase.
Bush has asked for the additional funds to cover military operations and reconstruction in Iraq and Afghanistan over the next year.
Published on Saturday, the poll results surely would add to the worries of the president.
Bush's approval rating has slipped one point to 52% from an earlier Newsweek poll conducted in August.
The approval rating for the president's handling of the Iraq situation also slipped to 51% from 54% in August.
The survey covered 1004 adults and has a 3% margin of error.