Rep. Tom CottonTom CottonGOP grapples with how to handle town halls Sanders: 'If you don't have the guts to face your constituents,' you shouldn't be in Congress Protesters crash McConnell's speech MORE (Ark.), the Republican candidate in the hotly contested Arkansas Senate race, declined to say what Republicans should do if President Obama takes new executive actions giving legal status to workers living in the U.S. illegally.

Cotton was asked about whether Republicans would consider impeaching Obama if the president took such a step. 

Fox News host Neil Cavuto pressed Cotton twice on the subject, the second time saying: "Republicans have sort of tiptoed around this idea whether they want to pursue impeachment. John Boehner says no. Would an action like that, you know, calling off the deportation of millions of illegals here, warrant such action?"

"Neil, I don't want to engage in speculation about hypothetical actions the president may or may not take," Cotton said. 

He emphasized the House vote last week to rein in President Obama's program deferring deportations for some in the country illegally.

 "What we did in the House last week was stay past our scheduled recess date and pass legislation that would stop exactly that kind of unilateral presidential amnesty by denying federal funding and federal resources to the president and all agencies to implement such an order," Cotton added.

Democrats have been playing up the possibility of impeachment and using the idea in fundraising pitches, leading to a record $4.8 million haul for House Democrats in one week in July. 

Most Republicans have sought to avoid the topic, believing it would only help Democrats. 

Speaker John Boehner (R-Ohio) has dismissed impeachment talk as a Democratic "scam."

Cotton has ramped up the immigration attack against his opponent, Sen. Mark PryorMark PryorCotton pitches anti-Democrat message to SC delegation Ex-Sen. Kay Hagan joins lobby firm Top Democrats are no advocates for DC statehood MORE (D-Ark.), launching an ad hitting the senator for supporting "amnesty."