Donald Trump and Sen. Ted Cruz. (Scott Olson/Getty Images)

Here is the question that will haunt Senate Majority Leader Mitch McConnell (R-Ky.) for the next 10 months: Will his blue-state Republican incumbents face the same disastrous fate in 2016 as Democrats did two years ago in “Romney-red” states?

A growing body of evidence suggests that the number of people willing to vote for one party for president and another for senator or congressman has shrunk to historically low levels, and 2014 was a near perfect storm that crushed Democrats. Then, Senate Republicans rode a wave of anti-Washington sentiment and growing fear over President Obama’s handling of terrorism into a historic nine-seat gain that handed them the majority, based largely on winning states that GOP presidential nominee Mitt Romney won handily in 2012.

Now Democrats see a map of Senate races that looks like the other side of the same coin, with Republicans playing defense in states that Obama won. Many Republican incumbents are trying to avoid the national limelight on issues that will dominate the presidential campaign.

Instead, they are eager to focus on local issues that play well in places like Marion, Ohio, and Rochester, N.H. Those two small towns recently played host to Sens. Rob Portman (R-Ohio) and Kelly Ayotte (R-N.H.), separate events on the same decidedly local theme: fighting heroin addiction.

Republicans will have to shift from aggressively playing offense in conservative-leaning states in 2014 to playing defense in Obama-leaning states in 2016. Their model may be Portman’s anti-drug push, including testifying Wednesday at a committee hearing with one of his constituents on his legislation to fight addiction.

Here are some of the most memorable campaign promises Republican presidential candidate Donald Trump has made since he declared his candidacy in June 2015. (Sarah Parnass/The Washington Post)

How Republicans handle that change will determine which party holds the Senate majority. The winners will control the chamber’s agenda and have enormous power to promote or block the next president’s legislative agenda.

The role reversal is not lost on the combatants.

“It is amazing. It’s almost the converse; it was seven Democrats who were up in Romney-red states [in 2014], and now you have seven of us up in states that President Obama won,” Portman said last week in an interview.

For months, as the Republican presidential primary process has drifted toward more-conservative, outsider candidates, GOP strategists have feared that the Senate and presidential maps of battleground states were so similar that an outside-the-mainstream nominee at the top of the ticket would sink their majority after just two years.

Some have begun to fight over who would be worse as presidential nominee, Donald Trump or Sen. Ted Cruz (R-Tex.), the two current front-runners. Other Republicans found solace in the fact that the Democratic contest has finally seen a surge from Sen. Bernie Sanders (Vt.), a potential nominee that many Republicans prefer at the top of the opposition ticket over former secretary of state Hillary Clinton.

With 54 Senate seats now in Republican hands, McConnell can afford to lose three if a Democrat wins the White House and four if the GOP wins the presidency; the vice president would be considered the tie-breaking vote in the case of a 50-50 split.

Six years ago, Republicans gained six seats but fell short of the majority. But because of that success in 2010, they are defending 24 of the 34 seats up for grabs in November.

The lack of ticket splitters may be particularly concerning for Republicans, given Obama’s success in states where GOP incumbents will face vigorous challenges. Some analysts think a possibly polarizing presidential nominee would be devastating for either party.

According to the American National Election Studies, 28 percent of the electorate in 1980 cast mixed ballots for president and their member of Congress, part of a 40-year stretch in which between 17 and 30 percent of voters split their tickets. But in 2012, just 10 percent of all voters split their ballot — 6 percent of Democrats voted for Obama and then voted for a Republican congressman, and just 4 percent of Republicans voted for Romney and then a Democratic congressman.

“It largely depends on the nominee. Trump and Cruz make it pretty challenging for Republican incumbents,” said Jennifer Duffy, senior editor of the Cook Political Report, an independent political analysis outfit. “How do they walk away from the nominee without alienating the base? How do they embrace the nominee without alienating moderates and independents?”

Democrats are already using Trump’s comments to formulate legislative amendments in an effort to force GOP incumbents to take stands on his ideas. Last week’s legislation to stem refugees from Iraq and Syria ground to a halt when Senate Minority Leader Harry M. Reid (D-Nev.) tried to offer an amendment on Trump’s proposal to ban all Muslims from entering the United States.

“This is more of a national campaign than many I have seen, because people are hurting,” said Sen. Charles E. Schumer (D-N.Y.), who is expected to succeed Reid when he retires and who hopes to take over a new majority in 2017. “I think it’s going to be very hard for them — given their voting records, all of which are quite close to the voting records, say, of Cruz — to divorce themselves from the national issues.”

Democrats, though, are battling history. Since 1956, the Senate majority has switched just once in 15 presidential elections. That was 1980, when Ronald Reagan swept into office with 12 additional Republicans.

Some Republicans think that presidential ballots give voters multiple options, allowing good candidates to break through in states that vote heavily in the other direction for president.

“You have two votes, so you can cast one of those votes for the candidate for president and still have a voice left,” Sen. Roy Blunt (R-Mo.) said. “If there’s no president on the ballot, you just have one way to send a message: We are fed up with this, and the only message we can send is through the House and Senate.”

Republicans have studied the 2012 victories of Sens. Heidi Heitkamp (D-N.D.) and Jon Tester (D-Mont.), despite Romney’s huge victories in their states. One particular area of focus is how they fought on local issues, especially in defining their opponents’ backgrounds. As Republicans tied him to Obama, Tester counterpunched with ads about a lawsuit his opponent filed against his local fire department.

Senior party strategists, therefore, expect Portman’s campaign to focus heavily on the record of his likely opponent, former governor Ted Strickland (D), while running the state — a time of high unemployment during the Great Recession. Ayotte is expected to try to contrast her record as state attorney general vs. her likely opponent, Gov. Maggie Hassan (D), particularly on the alarming heroin epidemic there.

But some of the big national issues will be unavoidable. On Thursday, Ayotte led a news conference excoriating Obama’s nuclear deal with Iran. “National security is going to be a fundamental issue in this election,” she said in a brief interview afterward.

She quickly noted that national security also has local ramifications in New Hampshire, beginning with funding for the Portsmouth Naval Shipyard. The question is whether these local issues can overcome the din of partisan presidential politics.

Republicans hope so, or else they could lose the majority.

“I think you can focus on areas where you may not have a Republican position, but you have a personal position,” Portman said, citing his record on trying to fight heroin addiction. “It’s part of who I am, and I’m going to keep doing it.”