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The National Football League on Wednesday handed out stiff penalties to members of the Saints football team for participating in the bounty program, where players were reportedly paid $1,000 or more for injuring a player from the opposing team. The NFL suspended Saints coach Sean Payton for all of next season and banned the team's former defensive coordinator, Gregg Williams.

Durbin commended the NFL for imposing the "historically stiff penalties" and for taking "swift and decisive action," but suggested there might still be room for federal legislation and regulations.

"I want to hear the policies and practices in each of the major sports and collegiate sports that are being put into place," Durbin said. "I want to explore whether federal legislation is required."

Vitter followed his first message with a second Tweet wondering where Durbin had been several years ago when players of from the Chicago Bears became embroiled in a drugs scandal.

"Jog my memory," tweeted Vitter. "Did Sen. Durbin call for a Senate hearing when his home state Bears were selling drugs?"

Durbin said his hearing will take place in the Senate Judiciary Committee, but he did not set a date.

Peter Schroeder contributed