On Wednesday, Rep. Steve King (R-IA) pointed out that Rep. Paul Ryan’s (R-WI) promise not to bring up a comprehensive amnesty during this Congress if he is elected as the next House Speaker does not take care of the concerns conservatives have about a potential amnesty bill in the next Congress.

In an interview with MSNBC’s Chris Matthews on Hardball, King said that Ryan’s past support for a comprehensive amnesty bill was “a big problem for me” and confirmed that Ryan told Republicans this week that he would not bring up a comprehensive amnesty bill while President Barack Obama is in office.

“He said that he would not consider any large immigration initiative while President Barack Obama is still in office,” King told Matthews.

King said that will take care of the concerns until Obama’s term ends, “but it doesn’t take care of the concerns in the next Congress, which likely will have the same Speaker as this one.”

Rep. Luis Gutierrez (D-IL) has called Ryan his “ally” in his quest for amnesty for all of the country’s illegal immigrants, and Rep. Ileana Ros-Lehtinnen noted that Ryan worked “every day” in 2014 to craft a comprehensive amnesty bill in the House.