INDIANAPOLIS, Indiana (CNN) --
Some of Sen. Barack Obama's best-known backers are urging Sen. Hillary Clinton to drop out of the race.
1 of 2 "The more people get a chance to vote, the better it is for our democracy," the New York senator and former first lady told supporters at a rally in Indiana, which holds a May 6 primary.
"There are some folks saying we ought to stop these elections," she said.
"I didn't think we believed that in America. I thought we of all people knew how important it was to give everyone a chance to have their voices heard and their votes counted." Watch Clinton say she's had the 'best time' »
Clinton has won primaries in the biggest states so far, but Obama has won more total contests and leads her in the race for delegates to the party's August convention in Denver -- where the Democratic nominee will be formally ratified.
Two of Obama's leading supporters, Sens. Christopher Dodd and Patrick Leahy, said Friday that Clinton should rethink her chances of overcoming that deficit and consider folding her campaign.
Leahy, of Vermont, said Clinton "has every right, but not a very good reason, to remain a candidate for as long as she wants to."
Speaking in Johnstown, Pennsylvania, Obama said he did not discuss Leahy's call for Clinton to drop out with the Vermont senator, who serves as chairman of the Senate Judiciary Committee.
"My attitude is that Sen. Clinton can run as long as she wants," the Illinois senator said.
"She is a fierce and formidable competitor, and she obviously believes that she would make the best nominee and the best president. I think that she should be able to compete, and her supporters should be able to support her for as long as they are willing or able."
Obama called fears that the Democratic Party would be damaged by a long campaign "somewhat overstated." But he added that both he and Clinton should avoid campaign attacks "that could be used as ammunition for the Republicans" in November.
A CNN/Opinion Research Corporation poll released Thursday suggests that the bickering between Clinton and Obama could affect Democratic turnout in November.
One in six Clinton supporters said they would not be likely to vote in November if Obama gets the nomination; an equal number of Obama's supporters said the same about Clinton.
Democratic Party Chairman Howard Dean said Friday that he would like the fight wrapped up before the Denver convention, and said party leaders have had "extensive discussions" with the Clinton and Obama campaigns about cooling down their rhetoric.
"I don't think the party is going to implode," he said. But he added that personal attacks "demoralize the base" and that campaigns should focus on issues like the economy and Iraq. E-mail to a friend