The former two-term governor was elected Tuesday to replace Sen. Olympia Snowe, who didn't run because of what she calls political gridlock in Washington.
In a phone interview Thursday, Woodward told The Associated Press that King won't carry a swing vote in the Senate, but being an independent "enhances his leverage."
He says King continues Maine's long tradition of independent senators. Although Snowe, Sen. Susan Collins and former Sen. William Cohen are Republicans, Woodward says they've all acted like independents.
Woodward will be in Waterville on Sunday to receive Colby College's Elijah Parish Lovejoy journalism award. He'll be back next Thursday to speak at the University of Southern Maine.