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On the Republican side, former Sen. Dan Coats and former Rep. John Hostettler are among those who were weighing the race before Mr. Bayh announced plans to retire.

With Mr. Bayh off the ballot, veteran political handicapper Charlie Cook declared that the seat now leans Republican. Another, Stuart Rothenberg, said he now considers the race a tossup.

Mr. Bayh hinted that he sees a future running a company, a charity or a university. But he also will be considered a candidate for Indiana governor in 2012, or even to make a run for the White House.

In a meeting between Senate Democrats and Mr. Obama earlier this month, Mr. Bayh revealed his frustration when he challenged the president to prove to voters that Democrats can get past politics and prove they can solve problems such as the budget deficit.

“Speaking to independents, conservative Democrats, moderate Republicans - people who know we have to do this - why should the Democratic Party be trusted? And are we willing to make some of the tough decisions to actually head this country in a better direction?” he said.

Mr. Obama replied with a stinging attack on Republicans’ failures to balance the budget under President George W. Bush and by blaming the GOP for the financial market collapse that the president said has tied his hands.

In the bruising 2008 Democratic presidential primary, Mr. Bayh endorsed Hillary Rodham Clinton over Mr. Obama, but he said in his speech Monday that his retirement is not a reflection on the president.

“I look forward to working with him during the next 11 months to get our deficit under control, get the economy moving again, regulate Wall Street to avoid future financial crises and reform education,” he said.

Mr. Obama released a statement praising Mr. Bayh for “reaching across the aisle” on big issues. He remained silent on the senator’s criticisms of the level of partisanship in Washington.