WASHINGTON - New England’s moderate Republicans, shoved out of power by two Democratic waves of anti-George W. Bush fervor, are scrambling to make a 2010 comeback, making early bids for congressional seats that GOP leaders say are critical to taking back majorities in the House and Senate.

In next year’s midterm elections, former representative Charlie Bass is exploring a run for his old New Hampshire seat, while his fellow Republican, former attorney general Kelly Ayotte, who was reappointed by a Democratic governor, is expected to draw bipartisan support for a Senate run, should she win the GOP primary in New Hampshire.

Rob Simmons, a former moderate Republican US representative from Connecticut, is seeking the nomination to challenge embattled Senator Chris...