WASHINGTON — Democrat Bob Tuke, an underdog from the start, still faces an uphill battle to unseat U.S. Sen. Lamar Alexander, R-Tenn., according to a Chattanooga Times Free Press statewide poll.

The poll shows Sen. Alexander, who is seeking his second term, leading Mr. Tuke, a Nashville attorney and former state Democratic Party chairman, 57 percent to 33 percent, with 10 percent undecided.

“The undecideds are probably going to break toward Tuke, but as long as (Sen. Alexander’s) base stays up in the high 50s, he’s in good shape,” said Brad Coker, managing director of Washington, D.C.-based Mason-Dixon Polling & Research Inc., which conducted the poll.

Mr. Tuke’s main problem appears to be name recognition. According to the poll, 54 percent of respondents said they are not familiar with his name, compared to just 8 percent for Sen. Alexander, a former governor, presidential candidate and University of Tennessee president.

“Building name recognition, by and large, takes a lot of time,” said Jennifer Duffy, senior editor of the nonpartisan Cook Political Report, which has rated Tennessee’s Senate race as solidly Republican.

“There would have to be a political implosion of the Republican Party that we probably haven’t seen since Watergate” for Sen. Alexander to lose, she said.

Sen. Alexander received a “favorable” rating from 54 percent of poll respondents.

The poll of 625 registered and likely voters in Tennessee was conducted from Sept. 22-24. It carries a margin of error of plus or minus 4 percent.

Mr. Tuke, however, said the poll numbers do not reflect his own internal polls that show him closer to Sen. Alexander.

Mr. Tuke’s campaign said Friday it had cut Sen. Alexander’s lead in half from June, according to a poll conducted this week by New York-based Democratic polling firm Global Strategy Group. That poll showed Sen. Alexander leading Mr. Tuke, 50 percent to 38 percent, and found Mr. Tuke’s name was recognized by 76 percent of respondents.

That poll of 600 registered and likely Tennessee voters was conducted Sept. 21-24 and includes a margin of error of plus or minus 4 percent.

“A thing to remember is, the polling that’s been done does not reflect young people,” Mr. Tuke said. “People under 30 tend to have cell phones, so they don’t show up on caller lists. It also way under-reports African-American voters, and it can’t pick up newly registered voters. Those populations are going to vote Democratic.”

Among Democrats in the Times Free Press poll, 10 percent said they supported Sen. Alexander, 76 percent supported Mr. Tuke and 14 percent were undecided.

Ninety-two percent of Republicans said they would vote for Sen. Alexander, compared to just 3 percent for Mr. Tuke, with 5 percent undecided, the poll showed.

Independents leaned heavily toward Sen. Alexander in the poll, 66 percent to 21 percent, with 13 percent undecided.

Poll respondent Ann Guthrie, 64, a self-identified independent voter from Cordova, Tenn., in suburban Memphis, said she would vote for Sen. Alexander.

“He’s been in Tennessee politics for a long time, and when he was governor, he did a good job,” said Ms. Guthrie, who runs a small interior design business.

But poll respondent John Northcote, 58, a Democrat and self-employed businessman living in Gatlinburg, Tenn., said Mr. Tuke could help bring change to Washington.

“We need to have a government that is working together to accomplish things, not to fight against things,” Mr. Northcote said.

“The way to do that is to put enough lawmakers that agree in the House and the Senate and the presidency. The Republicans had that for six years (from 2001-2006), and look at where we’re at now.”

Comments