Hillary Clinton badly needs an overwhelming victory in the West Virginia primary on Tuesday to stave off elimination in the Democratic race. She might just get it, according to a new poll released this morning.

The survey, conducted by Suffolk University in Boston, gave Clinton a 60 percent to 24 percent lead over Barack Obama, who leads in overall delegates and popular vote. John Edwards, whose name remains on the ballot despite dropping out in January, received 4 percent, while 2 percent had no preference; 8 percent were undecided; and 2 percent refused a response.

Two thirds of likely voters said Clinton should stay in the race, regardless of what happens on Tuesday, and only 24 percent said she should withdraw. And 72 percent said she is not hurting the Democratic Party by running in the remaining primaries, while 20 percent said she is.

The state's voter demographics -- older, whiter, more rural -- sets up well for Clinton. And in a sign of trouble for Obama, his favorability rating (44 percent favorable, 41 percent unfavorable) was far lower than in other states and nationally, according to the poll. Clinton's favorability rating was higher: 70 percent favorable, 21 percent unfavorable.

The Democratic nominee has carried West Virginia in eight of the last 12 elections, dating back to 1960, but the poll suggests Obama faces an uphill battle. "Barack Obama may have to write off West Virginia come November," said David Paleologos, director of the Suffolk University Political Research Center.

The poll was conducted Saturday and Sunday and has a margin of error of plus or minus 4 percentage points. Suffolk has had a reasonably accurate track record this primary campaign, except last week in Indiana last week, where its last survey gave Clinton a 6-percentage-point edge. She won by 2 percentage points.

Clinton also holds a wide lead in Kentucky, a state with similar friendly demographics which holds its primary on May 20.

The survey, conducted last week, shows her with a 58 percent to 31 percent lead over Obama, with 11 percent of voters undecided, the Lexington Herald-Leader reported Sunday.