WASHINGTON » Majority Democrats fought Republicans for control of the Senate today after a bitter campaign marked by roughly $1 billion in outside spending in competitive races from Virginia to Montana.

Republican Sen. Scott Brown, who stunned Democrats in January 2010 by capturing Sen. Edward M. Kennedy’s Massachusetts seat, was the underdog against Democrat Elizabeth Warren in one of the nation’s costliest races. The candidates shunned outside money but together spent $68 million on their campaigns.

Democrats currently hold 51 seats in the Senate plus two independents who caucus with them. Republicans have 47 seats.

A loss for Republicans early in Massachusetts would make their path to a majority harder. Their hopes suffered a major blow when GOP candidates in Missouri and Indiana made awkward remarks about rape and abortion.