“Our expectation is, is that by this change in the law, we can be in a position to resolve this issue in a way that is satisfactory to Poland, but also meets the security concerns of the United States,” Obama said.

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Sens. Mark KirkMark KirkGOP senator: Don't link Planned Parenthood to ObamaCare repeal Republicans add three to Banking Committee Juan Williams: McConnell won big by blocking Obama MORE (R-Ill.), Barbara MikulskiBarbara MikulskiThe Hill's 12:30 Report Senate swears in new members Van Hollen lands seat on Banking Committee MORE (D-Md.) and Reps. Mike Quigley (D-Ill.), Jan Schakowsky (D-Ill.), Dan Lipinski (D-Ill.) and Brian Higgins (D-N.Y.) have introduced the measure referred to by Obama. 

It would revise annual reporting rules for the visa waiver program by mandating that countries applying to the initiative have no more than 3 percent of its citizens overstay their visas. 

Right now, roughly three dozen countries are part of the waiver program, a number the bipartisan group of lawmakers expects would expand under their legislation.

"President Obama's announcement is a major success for the citizens of Poland and America," Kirk said in a statement. "I look forward to passing this legislation in the Senate and a quick signature from the President."