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Club for Growth Action, the “super PAC” arm of the influential anti-tax group, is going on television with $2 million in ads against Donald J. Trump in Illinois, where Republicans will hold a primary on March 15.

The ad push is the latest in a combination of efforts to thwart the Manhattan businessman’s quest for Republican nomination.

The $2 million will be spent on cable and broadcast ads statewide, according to officials with the group. The Club for Growth will also spend another $1 million in Florida on a separate ad buy against Mr. Trump.

“A big-government liberal at the top of the GOP ticket would cost Republicans the White House, the Senate majority, and, ultimately, the Supreme Court,” said David McIntosh, the president of the Club for Growth Action, describing Mr. Trump’s positions as a “shell game.”

The two ads that will air were also run by the group in Iowa before the caucuses. The Club for Growth was the first outside group to go on the air against Mr. Trump last year, with what was initially a limited ad buy in Iowa. They went back up in Iowa shortly before the caucuses, along with another ad by a super PAC supporting Senator Ted Cruz, Keep the Promise I, and Our Principles PAC, which was formed specifically to stop Mr. Trump.

The groups are all working at this point to deny Mr. Trump a sweep of victories on March 15 in the delegate-heavy states of Illinois, Ohio and Florida.