On The Early Show, co-anchor Harry Smith said to Clinton, "We talked to a lot of people in Ohio who said there really isn't that significant a difference between you two, and they'd like to see you both on the ticket."
"Well, that may, you know, be where this is headed," Clinton said. "But of course, we have to decide who's on the top of the ticket, and I think that the people of Ohio very clearly said that it should be me."
When asked about Clinton's comments, Obama said he was focused on winning the nomination and that it was "premature" to start talking about a joint ticket, reports CBS News' Maria Gavrilovic.
"You know we are just focused on winning this nomination," Obama said. "That's my focus. And you know I've said before I respect Senator Clinton as a public servant, ah - she's a tenacious opponent. I think it is very premature to start talking about a joint ticket."
On a night that failed to clarify the Democratic race, CBS News projected Republican Sen. had clinched the Republican nomination for president, securing more than the 1,191 delegates needed. McCain had 1,205 delegates while Huckabee had 231. Click here for the latest state-by-state tally.
"It's a very humbling thing, and I say that with all sincerity," McCain said of finally securing the nomination.
McCain won Republican primaries Tuesday in Ohio, Texas, Vermont and Rhode Island by large margins.
Clinton won primaries in Texas, Ohio and Rhode Island, halting Obama's winning streak. Obama won in Vermont.
Clinton's three triumphs ended a month of defeats for the former first lady, and she told jubilant supporters in Columbus, Ohio, "We're going on, we're going strong and we're going all the way." (
Obama sought to counter Clinton's claims that the night had been a campaign-altering event. "We have nearly the same delegate lead as we did this morning and we are on our way to winning this nomination," he told supporters in San Antonio, Texas. (
"Coming into the night, Clinton faced the prospect of increased pressure from within the party to rethink her commitment to the campaign if she failed to win both Ohio and Texas," said CBSNews.com senior political editor Vaughn Ververs. "After winning three of four primary contests, who's going to call on her to drop out now?"
Both Democrats insisted on Wednesday they had the best credentials to go head to head - or as Clinton put it "toe to toe" - against McCain.
In Texas, with all precincts reporting, Clinton led Obama 51 percent to 48 percent. With 100 percent of precincts reporting in Ohio, Clinton led 54 percent to 44 percent. With 98 percent in Rhode Island, Clinton led 58 percent to 40 percent. And in Vermont, Obama led 59 percent to 39 percent with 93 percent in.
Texas Democrats also held caucuses on Tuesday night, which will allocate 35 percent of the state's delegates, but final results were not expected until later Wednesday. An early count by CBS News showed Obama with a slight lead; 52 percent to 48 percent with just 36 percent of the votes in. It was too early and the margin too close for CBS to project a winner in the caucuses.
According to the latest CBS News estimate, Obama still leads in the overall delegate count, 1,541 to 1,438. See the latest state-by-state tally.
It takes 2,025 delegates to win the Democratic nomination, and slightly more than 600 remained to be picked in the 10 states yet to vote.