Sen. Hillary Clinton has widened her lead in the race for the Democratic Party's presidential nomination, according to the latest CBS News poll of Democratic primary voters. But more than one third of voters overall say they would definitely not vote for the former first lady.

In a hypothetical three-way contest, 51 percent of Democratic primary voters choose Clinton as the nominee. That's the highest percentage since CBS News started asking the question in the spring and an increase of seven points from September. Twenty-three percent back Sen. Barack Obama, while 13 percent support former Sen. John Edwards.

Sixty-four percent of Clinton's supporters say they "strongly favor" the former first lady, while 26 percent say they support her with reservations. Obama is strongly favored by 47 percent of his supporters, while 43 percent support the candidate with reservations.

Get Breaking News Delivered to Your Inbox

If Clinton becomes the Democratic nominee, more than 70 percent of Democrats say they will consider voting for her or definitely vote for her for president. Only 6 percent of Democrats say they would not vote for her.

But among registered voters overall, 36 percent say they would definitely not vote for Clinton. Twenty-four percent would definitely vote for her, 21 percent would consider voting for her, and 19 percent say it's too early to say.

Forty-six percent of registered voters believe that if Clinton is elected, she will divide Americans. Forty percent say she will bring Americans together.

Though Clinton is a practicing Methodist, three out of four registered voters do not think she has strong religious beliefs. Even a majority of Democratic primary voters - 63 percent - say her religious beliefs are not strong. Obama and Edwards are thought to be more religious than Clinton, though none of the three is thought to have strong religious beliefs by a majority of those surveyed.

Clinton is viewed favorably by 43 percent of all voters, while Obama is viewed favorably by 38 percent and Edwards by 30 percent. Significantly more Americans say they are undecided or don't know enough to have an opinion about Obama (37 percent) and Edwards (39 percent) than say the same about Clinton (16 percent).

When former Vice President Al Gore, who has not entered the race, is added as a choice for the Democratic nomination, he emerges as a serious contender. Gore garners support of 32 percent of Democratic primary voters, while Clinton gets 37 percent, Obama 16 percent, and Edwards 7 percent. Gore is viewed favorably by 46 percent of registered voters, his highest favorability rating since October, 2000.

Read the complete poll results here.