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. Click here for the latest state-by-state tally.had clinched the Republican nomination for president, securing more than the 1,191 delegates needed. McCain had 1,205 delegates while Huckabee had 231.
"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.
The two presidential contenders made the rounds of the morning network television news shows Wednesday, declaring only one thing certain - that the campaign would go on and that the next big showdown would occur April 22 in Pennsylvania.
McCain, whose grasp on the nomination once seemed a distant reach, was headed for the White House Wednesday to have lunch with President Bush and get his endorsement. Bitter rivals in the 2000 presidential primaries, the two have forged an uneasy relationship during Bush's administration and have clashed on issues such as campaign finance, tax cuts, global warming and defining torture.
Despite Clinton's victories Tuesday night, Obama came away with a large share of delegates, too, in counting that continued Wednesday.
"We still have an insurmountable lead," Obama said.
Clinton and Obama spent most of the past two weeks in Ohio and Texas in a bruising campaign, with the former first lady questioning his sincerity in opposing the North American Free Trade Agreement and darkly hinting he's not ready to be commander in chief in a crisis.
Based on their current delegate counts, neither candidate can win enough delegates in the remaining primaries and caucuses to secure the nomination without the help of nearly 800 party officials and top elected officials who also have a voice in the selection. On Wednesday, Clinton and her campaign clearly aimed their case at those so-called "superdelegates" - a strategy that could take the nomination fight all the way to the party's August national convention in Denver.
"New questions are being raised, new challenges are being put to my opponent," she said. "Superdelegates are supposed to take all that information on board and they are supposed to be exercising the judgment that people would have exercised if this information and challenges had been available several months ago."
She said voters are being drawn to her argument that she would be the better commander in chief, the best steward of the economy and that she can better confront McCain in the general election.
Obama countered that on a key national security issue - the war in Iraq - "she got it wrong" by supporting Mr. Bush's call for authority to use of force.
As for superdelegates, Obama said he expected them to rally around him.
"I don't think it will necessarily go to the convention floor," he told reporters aboard his plane before taking off from San Antonio for Chicago.
He also said he will challenge Clinton on her foreign policy credentials.
"Was she negotiating treaties? Was she handling crises? The answer is no," he said. "She made a series of arguments on why she should be a superior candidate. I think it's important to examine that argument."
The CBS News count does not include delegates from Florida and Michigan, who were penalized by the Democratic Party for moving up their primaries ahead of a schedule set by the Democratic National Committee. None of the Democratic candidates campaigned in either state. But Clinton, who won the popular vote in both state primaries, on Wednesday renewed her call for Florida and Michigan to be counted in the nomination race.
"It's a mistake for the Democratic Party to punish these two states," she said. "I don't see how a Democratic nominee goes forward alienating two of the most important states."
McCain surpassed the 1,191 delegates needed to win his party's nomination against odds that seemed steep only a few months ago, and all but impossible last summer.
Facing a couple of well-financed marquee candidates in a crowded field, the Arizona senator opened his comeback in New Hampshire's leadoff primary, rolled over Rudy Giuliani in Florida and finished off Mitt Romney after Super Tuesday on Feb. 5.
Huckabee's rise and fall by CBS News' Joy Lin, who was an embedded reporter on the Huckabee campaign)hung in until Tuesday night, gamely keeping up the fight weeks after dropping from long shot to afterthought. (read an analysis of