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In the Delaware race, Mr. Biden was supposed to be the perfect Democratic candidate to hold that seat. He has name recognition, he holds statewide office and he was expected to have all the financial resources he would need.

But in a letter to supporters, he said he had unfinished business as attorney general that would keep him out of the race for the seat his father held for 36 years.

“I cannot and will not run for the United States Senate in 2010. I will run for re-election as attorney general,” he said.

He said he will instead focus on “a case of great consequence” — that of Dr. Earl Bradley, a pediatrician who has been accused of sexually abusing dozens of his patients.

“One of the primary reasons I ran for attorney general was to protect the most vulnerable among us: children. As the father of two young children, I can think of no worse crime than those committed by child predators,” Mr. Biden said.

Sen. Thomas R. Carper, a Democrat and Delaware’s senior senator, said Mr. Biden “will have plenty of opportunities in the future.”

Sen. Ted Kaufman, the Democrat and former aide to the vice president who was appointed to his seat, repeated his vow not to run in this year’s election.

Democrats and Republicans have taken notice of Mr. Obama’s inability to help pull fellow Democrats over the finish line in campaigns.

Mr. McKenna said the Democrat in New Jersey tied himself closely to Mr. Obama and lost, the Democrat in Virginia distanced himself from the president and lost, and the Democrat in Massachusetts seemed unsure which direction to go — and also lost.

The president still has wide appeal for Democrats, but Republicans are overwhelmingly opposed.

Gallup, the polling organization, found that 88 percent of Democrats approve of the president at the one-year mark, but just 23 percent of Republicans approve — the largest partisan gap they’ve ever recorded at this point in a presidency.

“I think we live in a very divided country,” said White House press secretary Robert Gibbs in explaining the numbers.

Meanwhile, another poll, this one from the Robert Wood Johnson Foundation, which measured consumers’ views of health care showed enthusiasm for Democrats’ health care reform plans slipped in December, just as both the House and Senate were pushing for action.

The Associated Press said the poll, being released Tuesday, showed Americans were increasingly worried that the health care plans would hurt both their own and the country’s finances.