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Former Democratic Gov. Jeanne Shaheen ousted freshman Republican Sen. John E. Sununu in November, and both of the state’s Democratic House members — Reps. Carol Shea-Porter and Paul W. Hodes — have been mentioned as possible 2010 challengers to Mr. Gregg.

A coalition of liberal Democratic groups already has been running ads in New Hampshire to pressure Mr. Gregg to vote for Mr. Obama’s $819 billion economic rescue bill, which failed to get any Republican votes when it passed the House on Wednesday.

One scenario being discussed in Democratic circles has Mr. Lynch, a centrist governor who has made a point of working with Republicans, agreeing to select a senior Republican figure or a nonpartisan replacement for the last two years of Mr. Gregg’s term. The appointee would agree not to run in 2010.