With the field down to two, Barack Obama is feverishly pressing to make up ground against Hillary Clinton in the 22 states hosting Democratic primaries and caucuses Feb. 5, tapping a windfall of recent fundraising money to boost staff and buy up TV ad time.

Obama and Clinton head to Hollywood Thursday evening at 8 p.m. ET for the first debate of the campaign featuring just the two of them. John Edwards dropped out Wednesday without endorsing either candidate.

Obama is behind in the polls in delegate-rich California and most of the states voting Feb. 5, including New York and New Jersey, where Clinton is hoping to score valuable victories.

But fresh off a big win in the South Carolina primary Saturday, and aided by endorsements from Sen. Ted Kennedy and other party fixtures, the Illinois senator is looking for gains across the country.

Obama believes he can close the gap in California. Democratic sources unaffiliated with either campaign told FOX News overnight polls in the state showed wild swings, with Clinton and Obama trading the lead.

And Obama attempted to build on his momentum Thursday. Recognizing he has catching up to do among Latino voters -- who have trended toward Clinton in recent primaries -- Obama brought his multi-racial pitch to a technical college in downtown Los Angeles in the hours before the debate.

"When I talk about issues that affect the Latino community, and the black community and the white community, urban issues that affect all of us, this is not just the rhetoric of a campaign," Obama said. "The cause of my life ... the issues that are most pressing are the same ones that I was organizing around 20 years ago."

The Obama campaign announced Thursday morning it raised $32 million in January alone and attracted 170,000 new donors. The haul was the most money the campaign has raised in a single month and matched the Illinois senator's best three-month period last year, aides said.

The cash gives him a boost in the ad wars. Obama is already advertising in all but two of the Feb. 5 states, and the campaign plans to go on TV and radio airwaves in seven more states voting after Feb. 5, including Louisiana, Washington and Virginia.

Clinton is advertising in 12 Super Tuesday states, including New York.

The Clinton campaign released two new 30-second ads it will run in those states emphasizing the senator's tactics for dealing with a flagging economy, which has swiftly become a top issue in the campaign. One features a plunging skydiver as an announcer proclaims "our economy could be heading into free fall." The other shows her proclaiming a "can-do spirit" and vowing to "turn our economy around and build a new age of prosperity."

Both ads suggest she is the most qualified to tackle economic challenges.

Obama has also ventured into New York, forcing Clinton to play defense in the state that elected her twice to the Senate.

Like the GOP race, the Democratic contest has gotten more tense as the field narrowed.

The two remaining Democrats took swipes at each other in advance of the debate -- Obama said Wednesday that a Clinton presidency would be a step back to the 20th century, a reference to former President Bill Clinton's pledge to build a bridge to the 21st Century.

Clinton shot back that Obama was abandoning the politics of hope.

But Clinton has found herself defending the actions of her husband on the campaign trail. After Bill Clinton drew the scorn of several prominent Democrats for his aggressive tone in South Carolina, Clinton told ABC News' Cynthia McFadden in an interview that aired Wednesday she's sorry if anyone came away hurt.

"I think whatever he said which was certainly never intended to cause any kind of offense to anyone," Clinton said, "if it did give offenses then I take responsibility and I'm sorry about that."

McFadden asked: "Can you control him?"

"Oh, of course," Clinton told her.

Both campaigns concede that a clear winner in the Democratic contest is not likely to crystallize immediately after Feb. 5, since the states award delegates proportionally. That means the candidate on top after Feb. 5 may only lead in the delegate count by a slight edge, pushing the campaign forward to the late February and March primaries.

Clinton spokesman Phil Singer said the campaign was not concerned about Obama's fundraising haul in January, though the campaign would not release its own January numbers.

"We will have all the resources we will need to compete and win," he said.

FOX News' Major Garrett and The Associated Press contributed to this report.