If Ashley Judd decides to run for Senate next year, she will get more attention than perhaps any other Democratic candidate. But she’ll be far from the most likely Democrat to win.

The actress’s Twitter feed certainly lends credence to the idea that she’s running. Judd has been rooting for local Kentucky sports teams, talking about hymns she enjoys hearing in church, asking what Bible verses are on her followers’ minds, and offering innocuous political comments.

In other words, Judd is saying many things that convey an interest in the political scene but not much that will offend Kentuckians. The daughter and sister of country singers, Judd’s family name is as big as her own profile.

Judd vying to unseat an incumbent Republican senator isn’t as outrageous as it would first seem. Mitch McConnell’s numbers are terrible for someone with his length of service (he was first elected in 1984), leadership position (he is the Senate minority leader and it’s not inconceivable that 2014 could make him majority leader), and lack of major scandal.

A poll released earlier this year by the Louisville Courier-Journal found that only 17 percent of respondents definitely planned to vote for him while 44 percent said they would make their minds up when they knew more about their options. Tellingly, just 34 percent of Republicans said they would back him against any challenger while 51 percent of Democrats already planned to vote against him.

Public Policy Polling—a Democratic firm—calls McConnell the most unpopular senator in the country, with a 37 percent approval rating versus 55 percent disapproval. Only 33 percent of independents approve of the job he is doing. The Senate GOP leader is at nearly 30 percent disapproval among Republicans.

In 2008, Democrats tried to oust McConnell. He was reelected by an unimpressive 53 percent to 47 percent margin. By comparison, when Bob Dole was Senate Republican leader, he was reelected to his fifth and final term with 64 percent of the vote in Kansas.

Kentucky is a fairly conservative state, but not necessarily a Republican one. As of 2012, Democrats actually boasted about 500,000 more registered voters in the commonwealth than Republicans. Democrats control the state house of representatives, Republicans the state senate. Democrats hold the governorship and other statewide offices.

There is also the risk that an attractive celebrity opponent would bait the Republicans, whose Senate candidates have had some inconvenient slips of the tongue in recent years, to say things that are interpreted as demeaning to women. Failing to take Judd seriously would be a major tactical blunder.

But McConnell’s underlying weaknesses aside, Judd has her work cut out for her. Despite family roots in Kentucky, she actually lives in Tennessee. She is a strong supporter of President Barack Obama, who didn’t even break 40 percent of the vote there in 2012. It doesn’t take much imagination to see how her Hollywood resume could be used against her in a campaign.

BuzzFeed recently published an interesting piece on successful celebrity candidates of the past—Ronald Reagan, Arnold Schwarzenegger, Al Franken, Fred Thompson, Clint Eastwood, Sonny Bono. But all of them were involved in at least semi-serious political activism before running for office, and most of them had been engaged in issues of particular interest to the people whose votes they were seeking.

Reagan was a leading campaign surrogate for Barry Goldwater in 1964. Franken was writing political books. Schwarzenegger served on the president’s Council on Physical Fitness. Thompson was actually involved in Tennessee politics and minority counsel for the Senate Watergate Committee before he became an actor.

Judd, who has a degree in public administration from the Kennedy School of Government, is better known for global humanitarian work than politics. That might speak well of her, but celebrities’ charitable endeavors tend not to translate into elective office. The political causes she has most conspicuously embraced—stumping for Obama and pro-choice liberal Democrats backed by the feminist group EMILY’s List—seem a poor fit for the Kentucky landscape.

When Eastwood ran for mayor, he emphasized talking to local media outlets. So far, Judd hasn’t been shy about embracing national media coverage in the run-up to a possible Senate bid. Her most enthusiastic supporters in recent polls are young people and “very liberal” voters, neither a promising path to a majority in Kentucky.

McConnell can raise money but it will be difficult for him to generate enthusiasm. Judd can inject the race with both. But it could work both ways. McConnell has tried to protect his Tea Party right flank by building bridges to his junior senator, voting for Rand Paul’s budget, joining his popular filibuster, hiring his former campaign manager Jesse Benton.

A Hollywood liberal challenger could give McConnell fits—or give conservative Kentuckians a reason to vote for him.

W. James Antle III is editor of the Daily Caller News Foundation and author of the newly released Devouring Freedom: Can Big Government Ever Be Stopped?