WASHINGTON — The close race for majority control of the Senate comes down to whether Republican candidates in Massachusetts and Connecticut can win over President Barack Obama's voters and Democrats from Indiana to Arizona can impress Mitt Romney's GOP backers.

Ticket-splitting is vital to the prospects of Senate candidates in a half-dozen races in states that Obama and Romney are expected to win handily. These candidates are significantly outdistancing their parties' presidential nominees in polls, turning what should be an election-year rout into too-close-to-call contests.

With about three weeks to the Nov. 6 vote, Democrats hold a slight edge in keeping their majority in the Senate. GOP hopes have faded in New Mexico and Hawaii while incumbents in Florida and Ohio withstand an onslaught of outside spending to run ahead of their struggling rivals. In an unlikely scenario, races in Indiana and Arizona, once considered certain GOP wins, are competitive.

"The map has expanded over the election cycle," said Guy Cecil, executive director of the Democratic Senatorial Campaign Committee, who credited the class of recruits. "When the cycle started no one gave Democrats a shot at holding the majority."

Still, the mathematical equations of the election remain unchanged.

Democrats hold a 53-47 advantage in the Senate, counting the two independents, and must defend 23 seats to the GOP's 10. The Republicans need a net of four seats to grab the majority if Obama wins and a net of three if Romney captures the White House and Paul Ryan as vice president breaks a Senate tie.

Republicans are counting the open seat in Nebraska as a pickup and are bullish about holding Nevada despite a concerted Democratic effort. They're also upbeat about snatching Democratic seats in close contests in Virginia, Montana and North Dakota. Romney's first debate performance energized the party for the home stretch.

"There's renewed enthusiasm on our side," said Rob Jesmer, executive director of the National Republican Senatorial Committee. "It's filtered down to our Senate candidates. There's very good movement across the board."

In the lineup of ticket-splitting races to watch, one of the biggest surprises and promising opportunities for the GOP in the closing weeks of the campaign is Connecticut.

Former professional wrestling executive Linda McMahon, in her second Senate bid, is running even with three-term Democrat Rep. Chris Murphy in the Democratic-leaning state.

The wealthy McMahon is financing her ads, forcing the DSCC to spend $2 million and counting in a state that's solidly in the Obama column. This past week, the Democratic committee bought an additional $650,000 in ads while the Democratic group Majority PAC invested more than $500,000 to air spots to help Murphy. It's money the Democrats certainly would rather spend elsewhere.

The Republican nominee, who is on the air in the expensive New York City market, is using commercials to argue that she is not beholden to either party.

"Linda is an independent-minded leader who won't be swayed by partisan politics," says a woman in a testimonial commercial for McMahon. "Linda will be an independent voice in the Senate for all of us," says another woman.

Although Obama won Indiana in 2008, it's unlikely this year as Romney seems a probable winner along with Republican Rep. Mike Pence in his gubernatorial bid.

Yet Democratic Rep. Joe Donnelly is in a close race with Republican Richard Mourdock, a tea party favorite who unseated six-term Sen. Richard Lugar in the May primary. Donnelly has played up his moderate voting record in the House as a contrast to Mourdock. The Republican famously said after beating Lugar that bipartisanship meant Democrats siding with Republicans and that winning meant he would "inflict my opinion on someone else."

Indiana is a "conservative state but a state that looks for results, not strident partisanship, in the tradition of Richard Lugar and Evan Bayh," Donnelly said in an interview.

Lugar is backing the Republican but making no major effort to help the GOP candidate. Donnelly is hoping to sway some of the senator's GOP supporters, repeatedly referring to his work with the longtime lawmaker.

On Friday, Donnelly got some help from former President Bill Clinton who drew a crowd of 4,000 at the Hoosier Commonsense Rally.

"What is this idea that it's my way or the highway?" Clinton told the crowd. "I was raised to believe nobody's right all the time. Maybe Mr. Mourdock is, I don't know. He's way right all the time."

In Massachusetts, Republican Sen. Scott Brown also is talking bipartisanship in his race against Democrat Elizabeth Warren. Brown won a special election in January 2010 to fill the seat of the late Democratic Sen. Edward Kennedy, but this election he'll likely face 700,000 to 800,000 more voters, many Democrats or independents who favor Democrats.

Polls in the state show Obama with a hefty double-digit lead over Romney, a former Massachusetts governor. The same survey shows Brown and Warren in a tight race.

Not surprisingly, Brown tells viewers in a recent commercial, "To me, creating jobs is more important than what party you belong to. That's why one of the first votes I took as a senator was for a Democratic jobs bill."

Montana and North Dakota are expected to go for Romney, but split-ticket voting could lift first-term Democratic Sen. Jon Tester and Heidi Heitkamp, respectively. Republicans and Democrats say both have run near flawless campaigns to make their races highly competitive against a strong GOP political headwind.

Heitkamp, North Dakota's former attorney general, recently said she's "not in this for any reason other than solving problems."

"Our candidates have shown remarkable resilience," Cecil said. "Senate races are a choice between the two people on the ballot. They're affected by, but not determined by the presidential race."

The Democratic counterpoint to Connecticut is Arizona, where Democrat Richard Carmona, a former U.S. surgeon general, has surprised the GOP, riding a compelling up-from-the-bootstraps biography to a close race against Rep. Jeff Flake.

The National Republican Senatorial Committee recently purchased more than $130,000 of ad time, an investment that would have seemed unlikely two months ago. Rival ads about Carmona's character and temperament emerged this week, underscoring the increasingly tight contest.

In Maine, Republicans and GOP-leaning outside groups are running ads against independent Angus King, the former governor who is widely expected to caucus with the Democrats. Democrats are spending heavily on ads against Republican Charlie Summers. The Democratic candidate, Cynthia Dill, has the backing of state Democrats but has gotten little attention from national Democrats.

Americans Elect, a self-described non-partisan group that wanted to get a bipartisan presidential ticket on the ballot, recently purchased about $90,000 for direct mail in Maine in support of King.

Missouri remains a true wild card. Democratic Sen. Claire McCaskill, once considered the most vulnerable incumbent, got a fresh shot at re-election when Republican Rep. Todd Akin said women couldn't get pregnant in the case of "legitimate rape." Republicans, including Romney, called on him to quit the race.

Akin stayed in, securing the support of Newt Gingrich and Rick Santorum, state Republicans and a boost from religious leaders in a state that Romney should win easily. McCaskill recently launched a series of TV ads in which rape victims expressed outrage about Akin's remark and his opposition to emergency contraception.