(CNN) Brandon Presley's phone is ringing a lot these days. The Elvis relative has taken calls from top Democrats, like Senate Minority Leader Chuck Schumer, and the only Democrat in the state's congressional delegation, Rep. Bennie Thompson.

And they all have a message: This is the year a Democrat can win in Mississippi, especially if the GOP eats its own.

"Anybody that is a Democrat in the South can look to Alabama and finally see a light at the end of the tunnel," said Presley, who's been elected three times to the state utility regulatory commission, and whose grandfather was the brother of Elvis's grandfather.

The stunning loss last week of Roy Moore in deep-red Alabama has given Democrats new hope to do something once viewed as all but impossible: Win back the Senate majority. And to do that, they'll have to defend five of their incumbents in red states Donald Trump won handily in 2016. Plus, they'll have to pick up at least two GOP seats, and one of those seats almost certainly would have to be won in a state with a Republican-heavy electorate.

Mississippi remains a long shot for Democrats, but they believe they can replicate the Alabama formula: Hope that the staunchly conservative Chris McDaniel challenges Sen. Roger Wicker in the GOP primary, leaving the Republican incumbent weakened -- or defeated -- for a general election against Presley.

McDaniel, who lost a vicious Senate primary fight against Republican Sen. Thad Cochran in 2014, is not deterred.

"It's fair to say that I'm leaning strongly toward the US Senate seat," McDaniel, a state senator, told CNN. "Anybody that understands the Deep South recognizes that for a Democrat to be successful, it's going to take the most egregious allegations imaginable to upend the race."

That's music to the ears of Democrats, since Presley is only likely to run if there's a Republican primary.

Asked if Presley could win a head-to-head race against Wicker, Thompson conceded: "It will be tough." But he flashed a grin when asked about a matchup against McDaniel.

"I think when you picked flawed candidates, that is probably the biggest shortcoming," said Thompson, the state's lone congressional Democrat. "Absolutely," a Democrat could win statewide, he said.

Wicker says he's ready for all challengers and is prepared to mount an aggressive campaign for a third term.

"I've just been getting ready in general for a vigorous re-election," Wicker said.

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A broader strategy, but overconfident?

Democratic leaders say that the fight in the South is part of a broader strategy nationwide, vowing to compete all over the country.

Even if they don't win in conservative states, they hope that Trump's cascading unpopularity will turn the environment toxic for the GOP, forcing the party to spread thin its precious resources in a desperate fight to keep its narrow majority.

"We're going to be competing everywhere," said Maryland Sen. Chris Van Hollen, chairman of the Democratic Senatorial Campaign Committee. "One of the lessons from (Alabama) is that we should compete everywhere -- and anything can happen."

Still, Republicans say that Democrats are growing overconfident and are dubious they can raise the kind of money necessary to compete nationwide. There are still vulnerable Democrats who stand a serious shot of losing in Missouri, Indiana, West Virginia, Florida, Wisconsin, North Dakota and Montana.

Plus, they say that the Moore race was an anomaly: He was a highly controversial candidate with positions that put him on the far-right fringe -- compounded by accusations of sexual assault of minors and pursuing relationships with teenage girls.

"I think the Alabama race, what we saw there was a reaction to the candidate," said GOP Sen. Deb Fischer, who is up for re-election next year in the red state of Nebraska.

Colorado Sen. Cory Gardner, the chairman of the National Republican Senatorial Committee, said the Alabama race "was about a candidate. It wasn't about an agenda."

Gardner added: "I feel very optimistic for 2018."

Republicans, too, are confident they can hold onto open seats in deep red states, including if veteran Sen. Orrin Hatch retires in Utah.

In an interview, Hatch signaled he'd make a decision about his future in the new year, adding that he wants to run again while saying that he expected Mitt Romney to mount a bid if he retires.

"I'm leaning in favor of running, but you never know, my wife doesn't want me to run," Hatch, 83, told CNN. Asked about Romney's interest in running, Hatch said: "I think he would -- I think if I hang it up, he might run. I would hope so if I do hang it up."

Democrats on defense in Minnesota?

The GOP hopes it can snag a seat in deep-blue Minnesota now that Sen. Al Franken is resigning amid allegations he touched women inappropriately. Republicans hope that the former governor, Tim Pawlenty, may be convinced to run for the open seat next year.

"I'm hoping Gov. Pawlenty does" run, said former GOP Sen. Norm Coleman, who lost his seat to Franken in a 2008 cliffhanger.

Pawlenty told CNN last week that he is "politically retired," even as he left the door open for a return.

Arizona could go blue

Republicans recognize that traditional GOP states are no slam-dunk in a year when polls show voters backing Democratic control of Congress by wide margins, including a Monmouth survey last week that shows a whopping 15-point preference for Democrats on the generic ballot.

In Arizona, where Republicans could face a brutal Senate primary for the seat being vacated by retiring Sen. Jeff Flake, Democrats have a shot with a moderate Democrat, Rep. Kyrsten Sinema.

"If you have a Democrat that runs a good campaign, and a Republican that just drills down on the base like the president does, that's not a good formula," Flake told CNN when asked about the Arizona race.

Asked if he thought Sinema could win, Flake said: "I do."

Moreover, Democrats believe that in two other red states -- Tennessee and Texas -- there's at least an outside shot of pulling off an upset, especially in Tennessee, where former Democratic Gov. Phil Bredesen is mounting a bid for the seat being vacated by Sen. Bob Corker, where another bitter GOP primary is shaping up.

"Gov. Bredesen's a well-respected former governor," said Sen. Lamar Alexander, the Republican from Tennessee. "His biggest challenge will be persuading Tennesseans that they want to move Bob Corker's desk over to Chuck Schumer's side of the aisle."

And in Texas, Rep. Beto O'Rourke, a Democrat who is challenging Sen. Ted Cruz, says the results of the Alabama race gives voters a reason to believe that upsets are possible in unthinkable places, including his own. He says he's been campaigning in suburban, rural and ranching communities -- traditional GOP strongholds.

"Democrats haven't been showing up there; we're showing up," O'Rourke said. "And people are turning out, so I'm really encouraged. And I think the only thing that's really changed is now many more people see that this is possible."