There are a lot of rumors circulating that U.S. Sen. Judd Gregg (R-NH) might be nominated to be the next Secretary of Commerce. According to New Hampshire election, law if Gregg abandons his seat Gov. John Lynch will have the power to appoint someone to fill the seat. However, if Lynch decides to pick U.S. Rep. Paul Hodes (D-NH) or U.S. Rep. Carol Shea-Porter (D-Rochester) then their selections will spark a special election in their respective congressional district.
New Hampshire Law:
661:5 United States Senator. If a vacancy occurs in the office of United States senator, the governor shall fill the vacancy by temporary appointment until the next state general election, when a senator shall be elected for the unexpired term.
661:6 United States Representative. If a vacancy occurs in the office of United States representative, the governor with advice of council shall, as soon as practicable, have precepts issued to the selectmen of the towns and cities in the district where the vacancy exists directing them to call a special state general election on the day he designates to fill the vacancy. Such election shall be conducted as provided in RSA 661:11 and shall fill the vacancy for the unexpired term.