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Earlier this year, Illinois Attorney General Lisa Madigan ultimately decided to run for re-election, despite being courted by the White House to consider a run for President Obama's former Senate seat.
"She would have walked into the seat," White House Senior Advisor David Axelrod said in an article posted in The New York Times over the weekend.
Giannoulias said he's not surprised the White House courted her.
"It's well documented some folks in D.C." wanted to go with "her great name recognition," Giannoulias said Tuesday following a press event announcing a new plan to reduce the threat of "too big to fail" banking institutions.
In the same New York Times article, Axelrod -- whose former political consulting firm is advising Giannoulias' challenger, David Hoffman -- expressed concern that the upcoming trial for ousted former Gov. Rod Blagojevich could hurt Giannoulias' run.
Axelrod said that although Tony Rezko, a Blagojevich fundraiser now in jail, never contributed to Giannoulias, Rezko did receive loans from the Giannoulias family business, Broadway Bank.