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North Dakota Republican Gov. John Hoeven easily won the Senate seat of Mr. Conrad’s fellow Democrat, Sen. Byron L. Dorgan, in November, after Mr. Dorgan opted not to run again.

Though the announcement was not expected, Capitol Hill insiders said the 62-year-old Mr. Conrad’s decision last month to pass on the chamber’s Agriculture Committee chairmanship was one indication that he was considering retirement.

No clear Democratic successor has emerged to run, but North Dakota Republicans hopefuls expected to enter the race include state Attorney General Wayne Stenehjem and Public Service Commissioner Brian Kalk.

In Connecticut, Mr. Lieberman was already facing a challenger from the left: former Connecticut Secretary of State Susan Bysiewicz, a Democrat, announced this week she will run for the seat.

Though Mrs. Hutchison’s departure gives Democrats’ a better chance of contesting the open seat in Texas, they have a relatively weak bench, and the man seen as their best hope, former Houston Mayor Bill White, has said he will not run.

Mr. White was soundly defeated by GOP Gov. Rick Perry in the gubernatorial race last year.

Among the top potential GOP candidates for the Hutchison seat are Lt. Gov. David Dewhurst and former Texas Secretary of State Roger Williams, who just picked up the endorsement of former President George H.W. Bush.