Democratic presidential candidate Hillary Clinton's strong performance in the first Democratic debate earlier this month did not help boost her poll numbers, though she remains in first place for the Democratic nomination in a new CNN/ORC poll out Monday.

Clinton remains in the lead with 45 percent support among Democrats, while Vermont Sen. Bernie Sanders received 29 percent support. Vice President Joe Biden, who is still weighing a presidential bid, received 18 percent support. One percent of Democratic voters picked former Virginia Sen. Jim Webb, and former Rhode Island Gov. Lincoln Chafee, former Maryland Gov. Martin O'Malley and Harvard professor Larry Lessig each received less than 1 percent support.

Sanders was the only candidate to see a significant change in his support, which is up five points since mid-September. Clinton didn't see a significant change despite the fact that more than six in 10 Democrats who watched the debate said she did the best job (just 35 percent said the same of Sanders).

That might be the case because Democrats who watched the debate were more likely to view Sanders and Biden favorably. While Sanders is viewed favorably by 62 percent of Democrats, among Democrats who watched the debate, that number jumped to 84 percent. Biden is popular among 76 percent of all Democrats but scored 89 percent in favorability among debate watchers. Clinton's support is roughly the same in both groups.

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Sixty-one percent of those who watched the debate say Biden should stay out of the 2016 presidential race. Eighty-four percent of Democrats who watched the debate say they are satisfied with the options they have for their nominee. Among Democrats who didn't watch the debate, 64 percent are satisfied with their options.

Support for a Biden presidential bid is dropping among Democrats. In August, more than half of registered Democrats (53 percent) wanted him to jump in; now that number stands at 47 percent. If he decides not to run, more of his support goes to Clinton, who would have a 23-point lead over Sanders.

Clinton continues to be the candidate Democrats say is best prepared to handle the economy, health care, foreign policy, race relations, climate change, gun policy and even income inequality, though her lead is small (43 percent say Clinton is best able to handle it, and 38 percent say Sanders).

A new Monmouth University Poll came to the opposite conclusion about Clinton's performance: They had her support increasing from 42 percent last month, before the debate, to 48 percent in their poll released Monday. They also had Sanders with 21 percent support, largely unchanged from last month when he received the support of 20 percent of Democrats and Democratic-leaning voters nationwide.

Biden's support decreased from 22 percent in September to 17 percent in October, and as with the CNN/ORC poll they found that his support would largely go to Clinton if he decides not to enter the race.

Even if he does stay in, Monmouth's analysis suggests that Clinton would still maintain a lead over Biden if he decides to jump into the race. If people inclined to support Biden did switch their votes, she would lead with 42 percent support. Biden would be in second place with 27 percent support and Sanders would fall into third place with 20 percent support.

The next Democratic debate will be hosted by CBS News, on Nov. 14.