Republican Mark Kirk holds a modest 46% to 40% lead over Democrat Alexi Giannoulias in the race for the Illinois Senate following Tuesday’s party primaries.

The first post-primary Rasmussen Reports Election 2010 telephone survey of the Kirk-Giannoulias race finds just four percent (4%) of likely voters in the state prefer some other candidate, while another 10% are undecided.

Among voters not affiliated with either of the major parties, the Republican holds a sizable 59% to 22% lead.

In December, Giannoulias was up by three points over Kirk. In October, the two men were tied at 41% each. In mid-August, Kirk held a modest 41% to 38% lead over Giannoulias.

The two men, as projected in previous Rasmussen Reports surveys, defeated several challengers to win their respective party primaries on Tuesday. But while Kirk holds a six-point lead for now in the race for the Senate seat held by Barack Obama, he may still face an uphill struggle in a state that trends Democratic.

Kirk, a U.S. congressman, leads Giannoulias, Illinois’ current state treasurer, by a wide margin among male voters but trails his Democratic rival by 13 points among female voters.

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Fifty-five percent (55%) of Illinois voters have a favorable opinion of Kirk, including 17% with a very favorable view of him. He’s viewed unfavorably by 33%, with just eight percent (8%) who have a very unfavorable opinion. Twelve percent (12%) are still not sure what they think of Kirk at this point.

For Giannoulias, favorables total 46%, with 12% who regard him very favorably. He is seen unfavorably by 39%, including 18% with a very unfavorable view. Fifteen percent (15%) have no opinion of the Democratic candidate for now.

While native son Obama carried Illinois over John McCain by a whopping 62% to 37% margin in November 2008, he’s less popular in the state today. Fifty-four percent (54%) of Illinois voters approve of the job the president is doing while 45% disapprove. Those figures include 33% who strongly approve and 35% who strongly disapprove. Those figures are much higher than Obama’s ratings nationally in the Rasmussen Reports daily Presidential Tracking Poll.

The country’s continuing economic problems, the lingering 10% national unemployment rate, and the health care debate in Congress appear to be a drag on Democratic candidates in many parts of the country.

In Illinois, 45% rate their personal finances as good or excellent, while just 13% say they are poor. But only 20% think their finances are improving, while 42% say they are getting worse.

Forty-seven percent (47%) of Illinois voters believe it is possible to balance the federal budget without raising taxes, but 34% disagree. Forty-four percent (44%) favor an across-the-bard tax cut for all Americans, but 38% oppose such a tax cut.

Still, the majority (53%) of voters in Illinois believe cutting taxes is a better way to create jobs than increased government spending. Twenty percent (20%) believe increased spending is the way to go.

Sixty-nine percent (69%) trust the judgment of the American people more than that of the country’s political leaders when it comes to important national issues. Only 14% trust the judgment of the political leaders more.

Seventy-one percent (71%) of Illinois voters say the federal government has become a special interest group, and 67% think the government and big business often work together to hurt consumers and investors.

Forty-four percent (44%) say the United States and its allies are winning the war on terror. Twenty-five percent (25%) say the terrorists are winning.

However, Illinois voters are evenly divided over whether the United States is safer today than it was before the September 11, 2001 terrorist attacks. Thirty-eight percent (38%) say yes, but 39% say no.

Democratic Senate incumbents who currently trail their challengers include Harry Reid in Nevada, Michael Bennet in Colorado, Blanche Lincoln in Arkansas and Arlen Specter in Pennsylvania. Democrats Barbara Boxer from California, Evan Bayh of Indiana and Russ Feingold of Wisconsin find themselves in more competitive races than usual.

Republicans lead open-seat Senate races in Delaware, Florida, Kentucky, Missouri, New Hampshire, North Dakota and Ohio. A Democrat leads in Connecticut. Just after the upset GOP win in the Massachusetts special Senate race last month, political analyst Larry Sabato concluded that if the election were held now, “The (59-seat) Democratic majority in the Senate would be reduced to just 52 seats.”

Former state House Speaker Marco Rubio has now jumped to a 12-point lead over Governor Charlie Crist in Florida's Republican Primary race for the U.S. Senate.

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