Republicans may be emboldened to intensify conflicts with an unpopular president in the last years of his term, but they risk Obama's veto if they push too hard for lower taxes, fewer regulations and other conservative priorities. Trade agreements that Obama supports, and changes to the immigration system that many Republicans favor, could offer chances for agreements.

Uncertainties in several tight races meant there was a strong possibility that neither party would be able to claim a Senate majority by the morning after Election Day.

Republicans were all but assured of winning Democratic-held seats in West Virginia, Montana and South Dakota, and Democrats held out little hope of a victory in Arkansas.

Polls suggested that races for Democratic-held seats in Iowa, Colorado and Alaska have tilted the Republicans' way, too—although Democrats said their get-out-the-vote operation made any predictions unreliable.

Democratic incumbents faced competitive races in New Hampshire and in North Carolina where Democrats said they had an edge—and Republicans disagreed.

Strategists in both parties said Louisiana and Georgia were both likely headed for runoffs . The wildest wild card of all was in Kansas, where polls said 78-year-old Republican Sen. Pat Roberts was in a close race with independent Greg Orman.

Obama was back at the White House after making his final campaign appearances over the weekend. He raised tens of millions of dollars over two years for Democratic candidates, but in the races' final days most members of his party opted not to appear in public with him because of his poor approval ratings.

“There are two people on the ballot tomorrow: me and Scott Brown,” said Sen. Jeanne Shaheen of New Hampshire as she made the rounds of six campaign stops on the race's final full day.

North Carolina Sen. Kay Hagan was one Democrat in a marquee race quietly accepting a bit of last-minute help from the president. She has spent much of the year distancing herself from Obama, but her campaign sponsored a radio ad featuring Obama calling her a tireless leader “who shares our priorities.” It was unclear where Hagan's campaign was airing the ads, but other candidates have used similar ads to boost turnout among African-American voters still loyal to the president.

Also on the ballot were gubernatorial elections in 36 states.

Among the most closely watched is Wisconsin, where Republican Gov. Scott Walker is in neck-and-neck race with Democratic challenger Mary Burke. Walker, a favorite of conservative Republicans, is often mentioned as a potential candidate in 2016, but his White House chances would almost certainly evaporate if he lost on Tuesday.

In another hard-fought race, Florida Republican Gov. Rick Scott is facing a tough challenge from Charlie Crist, a former Republican governor-turned-Democrat.