Virginia's major-party candidates for governor stepped up their argument Wednesday on issues concerning illegal immigration and abortion that were raised a day earlier at a debate in Fairfax County.

Republican Jerry W. Kilgore and others backing his campaign criticized Democrat Timothy M. Kaine for what they said was Kaine's support for spending public money to establish a center in Herndon for day laborers, some of whom may be illegal immigrants. The issue has been hotly debated in Northern Virginia and came up again at the debate.

"I believe that government should never subsidize illegal behavior or those who are here illegally in this country," Kilgore told a group of college students at a higher education forum Wednesday at Virginia Commonwealth University in Richmond.

Also Wednesday, Kaine criticized Kilgore for refusing to say during the debate whether he would outlaw abortion if given the chance.

Debate moderator Tim Russert, the host of NBC's "Meet the Press," had asked Kilgore whether he would support state legislation outlawing abortion if the U.S. Supreme Court allowed states to do so. Kilgore dismissed the question as hypothetical but then answered a hypothetical question on taxes, as Russert pointed out.

"My opponent would not answer the most simple and direct question," Kaine said of Kilgore's response on abortion.

"It's a fundamental kind of character issue," Kaine said. "You tell people where you are, and you let them decide whether they like your answer or not."

Kaine added that "trying to duck it as a hypothetical question, I think, appeared to most people in that room as very shifty."

Kilgore's campaign expressed frustration with Russert's performance as moderator, accusing him of "obvious favoritism" to Kaine.

"The debate was moderated by Tim Russert, who at every turn, disregarded the agreed upon rules and time limit," Kilgore campaign manager Ken Hutcheson wrote in an e-mail to supporters.

"It was typical Tim Russert," Kilgore said Wednesday, adding that he thought he had answered the abortion question. "I've moved on. We've moved on," he said.

According to a copy of the debate rules released by the Kaine campaign, "the moderator also may ask questions of the candidates at whatever point the moderator deems appropriate."

Kilgore focused much of his attention Wednesday on illegal immigration, saying to reporters that it is a drain on taxpayers and that it was one of the topics "you're going to hear . . . daily."

He said any Virginia business that hires illegal immigrants should be punished.

"Businesses are supposed to check on the legal status of workers," Kilgore said in a statement. "If businesses are knowingly violating the laws of the United States, they should not be rewarded with state contracts or be receiving state tax credits or benefits."

The issue of illegal immigration was the topic of a telephone news conference organized by Kilgore's campaign with Dels. David B. Albo (R-Fairfax) and L. Scott Lingamfelter (R-Prince William), who rebutted Kaine's remark in Tuesday's debate that Kilgore's position on the day laborer center in Herndon was "mean-spirited."

Lingamfelter said that supporting the day laborer center was akin to supporting "illegal activity" and that Kaine "missed that. He's turning a blind eye towards the problem."

Kaine's press secretary, Delacey Skinner, said that the Republicans had mischaracterized Kaine's position on illegal immigration and day laborer sites and that Kaine has said the establishment of such sites is a local issue to be resolved by local officials.

"As usual, Jerry Kilgore is distorting the record," Skinner said. "Tim Kaine has very clearly said that . . . he supports the prerogative of local governments to handle the challenges that they see in their communities."

She added that Kaine also would come down on businesses that hired illegal immigrants.

"If we discover that businesses are willfully violating immigration laws or hiring undocumented workers, they should not receive state benefits for that behavior," Skinner said.

Staff writers Annie Gowen and Michael D. Shear contributed to this report.

Timothy M. Kaine talks with reporters after debating Jerry W. Kilgore, who he said "would not answer the most simple and direct question" on abortion. Kilgore said he will focus more attention on illegal immigration and criticized Kaine for his position on Herndon's support for a center for day laborers.