(CNN) - Sen. Chris Dodd on Sunday joined the chorus of Democratic leaders downplaying the idea of a joint ticket between Sens. Barack Obama and Hillary Clinton.
"These are two great candidates who fought very hard, but my sense is today that that probably won't be the ticket," Dodd said on NBC's "Meet The Press."
Dodd, who abandoned his presidential bid on January 3, said he thinks it's "very clear" Obama will be his party's nominee.
Dodd expressed confidence that his party would rally around Obama, despite the lengthy primary season.
Obama campaign chief David Axelrod on Sunday predicted the process would be over soon, but avoided talk of any potential running mates.
"We'll focus on the vice presidential choice at the appropriate time," he said on "Fox News Sunday."
Clinton campaign Chairman Terry McAuliffe has said a joint ticket would be a "great idea," but the New York senator's strategist on Sunday said "any talk of it is premature."
"I haven't discussed it with her. She hasn't discussed it with me. I've seen no evidence of her interest in it," he told Fox.
Senate Majority Leader Harry Reid said it's up to the candidates to sort out the ticket.
"Only two people can make that decision and that's Obama and Clinton. No one else can make it. If that happens, it happens, but it can only be with the two of them," he said on ABC's "This Week."
He said the extended fight for the Democratic nomination has been "great for the country," pointing to increased voter registration for his party.
Reid said people should "just relax" because the primaries will be over June 3.
The renewed buzz of what some have called the "dream ticket" comes as Obama closes in on the Democratic nomination in recent days.
The senator from Illinois last week had a double-digit win in North Carolina and a narrow loss in Indiana.
Obama holds a commanding lead in the number of pledged delegates awarded from primaries and caucuses: 1,592 to Clinton's 1,424.
Following a flurry of new endorsements over the past few days, he trails Clinton by just one in the race for superdelegates.
At the beginning of the year, Clinton led the superdelegate race by more than 100.
Superdelegates are party leaders and officials who vote for the candidate of their choice at the Democratic convention in August.
The focus of the Democratic race has largely turned to the superdelegates because they outnumber the remaining pledged delegates that are up for grabs.
According to CNN's latest calculations, Clinton has 273 superdelegates to Obama's 272.
The Democrats face off Tuesday in West Virginia, where polls show Clinton with a substantial lead.
Clinton has a 43-percentage-point advantage over Obama, 66 percent to 23 percent, according to a survey from the American Research Group released Friday.
The poll was conducted after Tuesday's primary results and carries a margin of error of plus or minus 4 percentage points.
"This state is really Hillary Clinton's wheelhouse. It's an older population, socially conservative, blue-collar workers," said Kennie Bass, a political reporter for WCHS in West Virginia.
Obama acknowledges that West Virginians favor Clinton.
"She is going to do very well in West Virginia and Kentucky. She will win those states, in all likelihood, by significant margins," Obama said this week.
Obama took a break from the campaign trail Sunday, spending Mother's Day in Chicago, Illinois.
Clinton had three stops scheduled in West Virginia ahead of the primary, and her husband, Bill Clinton, was campaigning for her in Oregon.