Rep. Walsh, gator doll in hand, calls for serious debate on immigration

"If it will take introducing legislation calling for moats and these gators to get you serious about you securing the borders, Mr. President, I'm game," he added.

Gators aside, Walsh criticized Obama for making only token gestures for resolving border issues that include rising drug violence spilling into Arizona.

"President Obama, why aren't you serious about securing the border?" he asked. "Why do you consult with Latino celebrities like Eva Longoria to get their take on immigration reform?"

Rep. Dan Lungren (R-Calif.) on Wednesday said he was "disappointed" in Obama's comments earlier in the week that seemed to ridicule Republican demands for border security.