Now that New Hampshire Gov. John Lynch is clearly out of the Senate picture in 2010, the door is open for the state’s two House members to consider challenging Republican Sen. Judd Gregg .

One of them, Democrat Paul W. Hodes , is openly gauging support, saying, “I am seriously considering a race for the U.S. Senate but my immediate focus is on the economic crisis and how to help New Hampshire middle-class families to recover.”

The state’s only other member of Congress also is a Democrat: Carol Shea-Porter , who like Hodes was first elected in 2006. Shea-Porter’s spokeswoman, Jamie Radice, reiterated Thursday that the congresswoman is focused on her current position and “working hard for the people of New Hampshire.”

Lynch told reporters this week that he doesn’t intend to seek his party’s Senate nomination. “Although I don’t know what I will be doing in 2010. I’m not going to run for the United States Senate,” he said.

Lynch, who as governor of New Hampshire is up for re-election every two years, had been regarded as the favorite candidate to challenge Gregg, who has indicated he will seek a fourth term in 2010. Lynch is the best-known Democrat in the state aside from freshman Sen. Jeanne Shaheen , who previously served as governor.

Dante Scala, University of New Hampshire political scientist, said Hodes’ campaign fundraising has been more robust than Shea-Porter’s, which may offer him an advantage. “Hodes probably has, on paper, a better chance than Shea-Porter,” in a Senate race, Scala said, but added, “not a huge advantage.”

A Dec. 30 poll from American Research Group showed Gregg with a strong lead over either House member in hypothetical match-ups. Gregg led Hodes 47 percent to 40 percent and led Shea-Porter 54 percent to 35 percent.

After the state’s two members of Congress, Scala notes, there is a dropoff of potential candidates with substantial name recognition.

Scala listed state lawmakers such as state Sens. Lou D’Allesandro and Margaret Wood Hassan as potential candidates, but added that the move from state Senate to U.S. Senate is a “big jump.”

Candidates who tested the waters for a 2008 Senate bid are also mentioned as possible Gregg challengers, including: former Portsmouth city Mayor Steve Marchand; business consultant Katrina Swett, wife and business partner of former Rep. Dick Swett; and Gary Hirshberg, the wealthy president and chief executive officer of the Stonyfield Farm dairy products company.

Any serious New Hampshire hopeful has to consider electoral prospects against the backdrop of a changing demographic — an influx of residents from Massachusetts and other neighboring areas who do not fall in line with the Yankee Republicans who have deeper roots in the state.

Over the past two election cycles, Democrats have won control of the state legislature, knocked both Republican House members out of office and ousted one-term Republican Sen. John E. Sununu last November in favor of Shaheen.

That trend is here to stay, Scala said, and it works against Gregg. But unlike Sununu in 2008, Gregg begins his race ahead in the polls and appears unlikely to face a candidate with a strong statewide profile.