"Time is what people should be playing for," Brady said, "because maybe that will help resolve things and in a way, we're jumping the gun here. It's still only March 20 and usually by this time, historically, we haven't known who the nominee was."
Political strategist Michael Feldman said also that letting the clock run out could be the party's best bet.
"There's a process at work, and there are voters who are voting and ultimately these things tend to tip," said Feldman, who served as a senior adviser in the Clinton-Gore White House. "They tend to tip in the direction of one candidate or the other and the outcome is based on the back and forth that these two historic candidates running historic campaigns have been having for the last year."
Said Brazile, "This is a race. And in the middle of the race I don't see why we should try to alter the rules because it's making us uncomfortable."
Feldman believes the fight to the finish is good for the party. "It may not be neat and it may not be clean, but at the end of the day it produces a stronger nominee and has behind it more energy and more excitement in all the ways you measure that," he said.
Feldman favors a more "organic" outcome, where the pledged delegates and superdelegates come to a consensus over the course of the primary season on which candidate has the best chance come November.
He doesn't see an outcome where "a couple of people get together -- whoever they may be, whatever their stature may be -- to get in and decide the outcome. It's just not how it's done and it doesn't seem to me that that is a likely outcome."
In Wednesday's New York Times, Tennessee's Democratic Gov. Phil Bredesen floated the idea of a convening of superdelegates following the nation's last primary June 3 so that the party could unify before the summer months behind the candidate.
In an interview with ABC News, Bredesen, who is one of the Democratic Party's 795 superdelegates, more than 40 percent of whom have not announced candidate affiliations, said his reasoning was born out of the concern that Democrats could see "lost opportunities" if the nomination battle makes its way to the party's August convention.
Bredesenl said the party must pull the trigger, to take the reins of the process and lead.
"It has to be the DNC. Only the DNC has the standing to make this happen," he said.
"I think in the case of Gore and Carter and others, they're the grand old people of the party and their council on these things would be very helpful and useful," he said. "But ultimately, this is about the party. And the party gets a candidate chosen and gets that candidate positioned to win the election."