WASHINGTON — President Bush’s popularity ratings have slumped to an all-time low and are beginning to weigh down Republican presidential candidates who are now trailing their Democratic rivals in the 2008 White House race for the first time.

According to a Newsweek poll, Mr. Bush’s approval rating stands at 28%, making him less popular than his father at his nadir and as disdained as President Carter was at the height of the Iranian hostage crisis in 1979.

“The Republican brand is pretty seriously degraded,” said Frank Luntz, a leading Republican pollster. “At these levels, the American people are saying they’ve had enough and want a change. It gets to the point where it overwhelms any individual popularity a Republican candidate could have. I can make a case for a Republican winning with Bush at 33%. I cannot make a case for one winning with Bush at 28%. If this does not change, Republicans are heading for a colossal failure in 2008.”

Despite running 12 percentage points behind Senator Clinton in the Democratic stakes, Senator Obama leads the top Republicans by wider margins than the former first lady — a factor that could sway Democrats who fear Mrs. Clinton is too polarizing a figure.

According to the poll, Mr. Obama would defeat Mayor Giuliani, the Republican front runner, by 50% to 43%, Senator McCain by 52% to 39%, and Mitt Romney by 58% to 29%. In recent months, polls had shown Messrs. Giuliani and McCain defeating leading Democrats.

Mr. Obama also was top of the list in terms of being seen as the most optimistic candidate — a key sign of electability. More than half of voters view him as optimistic, compared to 46% for Mrs. Clinton and 45% for Mr. Giuliani.

The poll was taken before and during last week’s first Republican presidential debate and partly accounts for why the candidates chose to mention Mr. Bush by name just once while evoking President Reagan 19 times.