WASHINGTON — As David Perdue campaigns throughout Georgia, the Republican candidate for Senate describes a struggling economy and people yearning for good jobs.

It’s not the emphasis that his fellow Republican, Gov. Nathan Deal, wants to hear.

Deal is battling for re-election while Democrats emphasize the economy and remind Georgians that they have the nation’s highest unemployment rate.

Georgia isn’t the only state where a governor on the ballot could conceivably undermine his party’s Senate nominee, or vice versa. Strong governor-senator links are by no means certain. But even a small drag could affect the GOP’s bid to gain six new Senate seats and take control.

Perdue constantly criticizes President Barack Obama, as do Republican Senate candidates in every contested race. Much of the criticism focuses on the economy, and Perdue portrays himself as a better job-creator than Michelle Nunn, his Democratic opponent.

Deal, meanwhile, talks of a brightening economic picture as he tries to hold off Democrat Jason Carter, grandson of former President Jimmy Carter.

“This is a state that is certainly rebounding,” Deal tells voters. He says Georgia is rated “the best state in the nation in which to do business.”

Democratic consultant Tharon Johnson says Perdue and Deal are sending a mixed message that’s likely to confuse, and possibly turn off, voters.

“Deal talks about Georgia being number one for business, and that may be true,” Johnson said. “But we’re also 50th in unemployment. Perdue touts his business acumen, but he outsourced jobs. There’s a disconnect.”

At least three other states have embattled governors whose campaigns possibly could hurt their party’s Senate nominee:

It’s hard to believe that a Republican governor and senator are struggling for re-election in one of the nation’s most reliably GOP states. But they are, and national Republicans are pouring in resources they had hoped to use elsewhere.

Gov. Sam Brownback, a former senator and presidential candidate, is revered in some conservative circles. As governor he launched a “real live experiment” with sharp tax cuts, which he predicted would spur the economy.

But state revenues dropped steeply, leading to big budget shortfalls and spending cuts that have angered many Democrats, independents and moderate Republicans.

Sen. Pat Roberts, a solid congressional conservative since 1981, shifted further to the right to fend off a tea party challenger in the GOP primary, as he campaigned for a fourth Senate term. Once he got the nomination, Roberts began coasting. That helped independent Greg Orman build a viable challenge, which Republican operatives are now scrambling to overcome.

Democrats hope mainstream Kansas Republicans will punish Brownback’s overreach, and possibly put Roberts into the same box.

Travis Smith, a Kansas GOP strategist, thinks that is unlikely.

Brownback’s and Roberts’ problems, he said, “are just so different.” Roberts is scrambling because he is seen as out of touch with Kansas, Smith said, and Brownback is endangered because of unpopular spending cuts in education and other services.

Both, however, “will be affected by the turnout factor,” Smith said, and it’s crucial that Republicans avoid a disgruntled base that stays home.

Republican Gov. Sean Parnell faces a surprisingly tough road to re-election in this heavily GOP state, while Republicans hope to oust first-term Democratic Sen. Mark Begich. Parnell’s problems include accusations that he dithered in the face of reported sexual assaults in the Alaska National Guard.

The state’s Democratic nominee for governor dropped out of the race and became independent Bill Walker’s running mate. Parnell’s critics hope the pairing will unite enough unaffiliated and Democratic voters to overcome the state’s traditional Republican tilt.

Even a modest anti-GOP surge could hurt Senate nominee Dan Sullivan.

Ethan Berkowitz, a Democrat who ran against Parnell in 2010 and was a state legislative leader, said conditions are ripe for a good Democratic turnout. Ballot initiatives dealing with labor, the minimum wage and the environment should energize the liberal base, Berkowitz said, and Begich’s ground forces “are everywhere.”

The partisan dynamics are reversed in Colorado, where a Democratic governor’s struggles conceivably could hurt his party’s senator.

Republicans say John Hickenlooper has been an indecisive governor who has not done enough to revive the economy. They relentlessly tie first-term Sen. Mark Udall to Obama, whose approval has sagged in a state he carried twice.

Nonpartisan pollster Floyd Ciruli said Hickenlooper has a greater appeal among moderates than does Udall, and it’s unclear how much their fates might be combined, if any.

“The informed conversation on the street is that Hickenlooper will make it,” Ciruli said, while Udall is seen as struggling against Republican Rep. Cory Gardner.

Cassidy reported from Atlanta.