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GREENVILLE, N.C. (CBS) ― The Democratic chase for the White House is now just a day away from another milepost.

North Carolina and Indiana hold primaries Tuesday and the two candidates both see the outcome as crucial.

Illinois Sen. Barack Obama bluntly told an Indiana crowd yesterday, "I need your help." New York Sen. Hillary Clinton told a cheering audience in Fort Wayne, "This is the final push."

"I think we've made up a lot of ground in the last weeks," Clinton told CBS News' The Early Show. "These are two states everyone said my opponent would win handily and I think we've turned them into very competitive contests."

"Every state's been important, every contest's been important," Obama said, also on The Early Show. "Obviously, Indiana and North Carolina are a couple of big states that I think represent what people are worried about across the country."

The two darted back to North Carolina for some last-minute campaigning, with polls showing Clinton chipping away at Obama's advantage. It was a brief diversion from the more competitive Indiana, where both planned to return by nightfall.

"In the end of the day, you don't hire a president to make speeches, you hire a president to solve problems," Clinton told a couple hundred people in a gymnasium at Pitt Community College, pressing her claim of experience.

She also kept up her populist pitch and call for a summertime suspension of the federal gas tax to help people facing rising fuel prices. "Let's listen to what the people are telling us," Clinton said, "because if we listen, we will hear this incredible cry."

Elsewhere, Obama campaigned among white, blue-collar workers in Evansville, Ind., before flying to North Carolina. The Democratic front-runner noted that the polls are very tight and the day's schedule had him "bouncing back and forth" between the two states.

"We're working as hard as we can and I desperately want every single vote here, in North Carolina and in Indiana," the Illinois senator said during an appearance at a construction site.

Later at a labor hall, Obama said he would make good on his campaign pledges. "I'm going to be a partner with you," he said. "I'm going to be following through. But I need your help."

In both states, Obama was trying to recover from a difficult period and put Clinton away after a difficult 16-month fight that has split the party. The former first lady, meanwhile, hoped to hang in the race with a win in one, maybe two states.

Television ads, automatic phone calls and mailed literature flooded both Indiana and North Carolina in the run up to Tuesday while thousands of volunteers for both candidates canvassed countless neighborhoods knocking on doors. With far more cash on hand, Obama outspent Clinton by an estimated $4 million to $5 million — roughly a third more — on TV ads in both states combined.

But no matter what happens tomorrow, Clinton and Obama say they'll press on. Both candidates took their fight over gas price relief to the morning talk shows Monday.

The two White House hopefuls expressed confidence in their chances of winning the Tuesday contests, but refused to predict that voting this week would be decisive enough to end the primary fight and begin the general election against GOP nominee John McCain.

On NBC's "Today" show, Obama predicted that after the final contests June 3 in Montana and South Dakota, "We will be in a position to make a decision who the Democratic nominee is going to be," he said. "I will be the Democratic nominee."

Clinton refused to predict Tuesday's results, but said her campaign has made up some ground after falling behind.

"I think we've closed the gap," she said on CNN's "American Morning."

Much of the exchange Monday centered on proposals Clinton has embraced to give drivers some relief from soaring gas prices. Clinton pushed her plan for a summer suspension of the gasoline tax, which she would pay for with a windfall profit tax on oil companies.

Obama called that plan a gimmick, and many economists expressed skepticism. In a CBS News/New York Times poll released Sunday, 49 percent of voters said they thought lifting the gas tax for the summer was a bad idea. Only 45 percent thought it was a good idea.

"I think a lot of people don't understand my plan," Clinton responded on The Early Show. "I want the oil companies to pay that $8 billion this summer instead of having the money come out of the pockets of consumers and drivers."

For his part, Obama rolled out a new TV ad for Indiana and North Carolina that derided "Clinton gimmicks that help big oil."

"She is doing what Washington usually does - pretending to do something with the suspension of the gas tax," he said on The Early Show.

Asked to respond to Obama's criticism, Clinton on Sunday had said: "I'm not going to put my lot in with economists because I know if we did it right ... it would be implemented effectively."

Does that mean she would not, as president, seek the advice of economists, Clinton was asked Monday on NBC?

"Oh no, of course not," she replied.

Obama is also zeroing in on a Clinton threat to "totally obliterate" Iran if it attacked Israel. Obama said the Iran threat amounts to Bush-style "bluster and saber rattling."

Defending her earlier Iran comment, Clinton said she doesn't think Iran would attack Israel, but wants to make the consequences "abundantly clear."

Bill Clinton, who has been perhaps the most active campaigner in the state, also planned nine stops of his own in the eastern and central parts of North Carolina on Monday.

"If you send her a big vote here, you will send a message heard around this country: 'We want to win the White House to change this country, and she's our girl,"' Clinton said.

Obama's wife, Michelle, scheduled stops in Fayetteville and Charlotte.

Obama is ahead in the hunt for convention delegates - 1,737 to 1,601, according to the latest CBS News count - but he has faced a spate of troubles over the past month. That has Clinton sensing an opening. Still, the delegate math works in Obama's favor, and it will be difficult for Clinton to overtake him.

In the CBS News/New York Times poll released on Sunday, Obama also has good news in an increased national lead over Clinton. Among Democratic primary voters (those who have voted or plan to vote in a Democratic primary) Obama now leads Clinton by twelve points, 50 percent to 38 percent.

(© 2009 CBS Broadcasting Inc. All Rights Reserved. This material may not be published, broadcast, rewritten, or redistributed. The Associated Press contributed to this report.)