Updated: Oct. 11, 2010 12:48 p.m.

CHICAGO (CBS) – Columbus Day. For some, it’s a time to relax, but not if you’re running for U.S. Senate in Illinois.

CBS 2’s Dana Kozlov reports the next three weeks will be filled with constant campaigning.

The two major-party candidates, Democrat Alexi Giannoulias and Republican Mark Kirk, are down to the critical final weeks to win votes. And right now, according to a slew of polls, they are in a virtual dead heat for the seat.

Kirk says he knows it will be a fight to the end. Giannoulias says he’s encouraged by a climb in some of the polls that show him a couple points ahead.

Both walked in the Columbus Day Parade in Chicago, a favorite stomping ground for politicians. It followed a Sunday morning “Meet the Press” debate which found both on the defensive — Giannoulias about his family’s failed bank and its ties to a known criminal and Kirk about the embellishment of his military record.

None of these issues are new but could prove to be deciding factors among one very important group: suburban women.

“How suburban women vote will be crucial,” says Paul Green, a Roosevelt University political studies professor.

Those who’ve made up their minds are already casting ballots. But Green says winning over those on the fence and getting them to vote will be key, here and across the nation.

“Illinois is one of the few and I mean few, true toss-up states,” says Green. “The future of power over the next two years for the U.S. Senate could depend on Giannoulias vs. Kirk.”

On Sunday, Giannoulias and Kirk appeared on NBC’s “Meet the Press” for the first of three debates. The two candidates are deadlocked in the polls.

LISTEN: Newsradio 780’s Steve Miller Reports

In the debate, moderator David Gregory honed in on the candidates’ weaknesses. For Giannoulias, it was the lending practices at his family’s failed Broadway Bank.

“Did you know that there were crime figures that you were loaning too?” Gregory asked.

“I didn’t know the extent of their activity,” Giannoulias said.

Giannoulias says he wasn’t intimately associated with the deals and that you can’t always vouch for the character of bank clients.

On Monday, Giannoulias clarified his comments. He said in a “perfect world” those weren’t the “kind of people that my father wanted to do business with.”

He called it a “little offensive” for Republicans to cherry pick a couple of people from the thousands of customers at the bank his late father founded. Broadway Bank failed earlier this year.

Meanwhile, Kirk was on the defensive too for embellishing his military accomplishments.

“Well, I made mistakes with regard to my military misstatements,” Kirk said. “I was careless, and I learned a very painful and humbling lesson.”

Gregory asked if Kirk claimed he was once shot at in Iraq when in fact, he was not.

“Well, for example, when you’re flying over Iraq as a big NATO strike, usually the Iraqis, opened up on us, but whether the squadron came under fire or not, it’s very confusing,” Kirk replied.

What is not confusing is the candidates different views of the economic stimulus plan. Kirk called it a failure.

“First of all, we recognized that the stimulus has largely failed,” Kirk said. “The very small part of it, it even went to infrastructure development projects. It didn’t answer the question, what happens when all the borrowed money runs out.”

But Giannoulias credited the stimulus with rescuing the economy from an even worse catastrophe.

“I think the bigger question is what would have happened, and it wasn’t flawlessly done. But if you take a look at what would have happened, I mean, do we need to see soup lines down the street to figure out what would have happened?” he said. “We avoided it, and all of the economists will tell you that millions of jobs were saved because of the recovery act. And we avoided a second Great Depression.”

Green Party candidate LeAlan Jones and Libertarian Mike Labno are also in the race.

(TM and © Copyright 2010 CBS Radio Inc. and its relevant subsidiaries. CBS Radio and EYE Logo TM and Copyright 2010 CBS Broadcasting Inc. Used under license. All Rights Reserved. This material may not be published, broadcast, rewritten or redistributed. The Associated Press contributed to this report.)

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