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Two polls released on Wednesday showed Republican Congressman Mark Kirk with a narrow advantage over Democratic State Treasurer Alexi Giannoulias in the race for President Obama's old Senate seat in Illinois.

The Illinois Senate race has remained tight since the summer, and Kirk leads by a slim margin of 1.8 percent in the latest RealClearPolitics polling average.

In a Rasmussen Reports poll, Kirk had the support of 44 percent of likely voters, while 40 percent backed Giannoulias. Four percent of voters supported Green Party candidate LeAlan Jones, 8 percent said they would vote for another candidate, and 5 percent remained undecided.

Kirk led 42 percent to 40 percent in a Public Policy Polling (D) survey released Wednesday. Jones earned the support of 4 percent of voters, while Libertarian candidate Mike Labno had 3 percent.

Rasmussen surveyed 750 likely voters for its poll, which had a margin of error +/- 4 percent. PPP (D) surveyed 557 likely voters, and its poll had a margin of error of +/- 4.2 percent.

The PPP (D) poll was conducted Thursday through Saturday, and the Rasmussen poll was conducted on Monday, a day before Kirk and Giannoulias squared off in their second televised debate in Chicago.

Tuesday's debate was marked by the kinds of assaults on each candidate's character that have saturated the Illinois airwaves in attack ads for months.

Kirk, who has been criticized for embellishing his military record as a Naval Reserve intelligence officer, refused to answer when Giannoulias prodded him about whether he had been shot at during combat stints in Kosovo and Iraq, as Kirk has previously stated.

"I have put my life on the line for the United States," Kirk said. "You were back in the rear with the gear."

Giannoulias shook his head and noted that his opponent was refusing to answer the question.

When it was his turn to go on the attack, Kirk hammered Giannoulias for the failure of his family-owned bank and its previous loans to mob figures.

"When you saw the Broadway Bank collapse, you took no responsibility whatsoever," Kirk said.

President Obama spoke at a fundraiser on behalf of Giannoulias earlier this month, and Kirk sought to tie his opponent to the White House's economic policies.

"I am the only candidate in this race who will vote to spend less, borrow less, tax less," Kirk said.

But in this Democratic-leaning state where Obama still maintains a home court advantage, Giannoulias countered by accusing Kirk of supporting failed Bush administration policies and mentioning the attack ads that have been aired on Kirk's behalf by an outside group headed by former Bush administration official Karl Rove.

"We can't afford to let Karl Rove come to town and steal these elections," Giannoulias said.

The Illinois Senate candidates will meet for a third and final debate on Oct. 27.