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Cruz Rejects Calls To Shut Down Government Over Immigration

AP Photo / Jim Cole

While Cruz is denying any such plans, multiple of his Republican colleagues have suggested that they may link an immigration measure to a continuing resolution to fund the government of Obama uses his executive power to delay the deportations of undocumented immigrants.

Rep. Steve King (R-IA) last week said that "all bets are off" if Obama signs an executive order.

And both Senate Minority Leader Mitch McConnell (R-KY) and Sen. Marco Rubio (R-FL) have suggested the GOP may link an immigration measure to a bill to fund the government if Obama acts on his own.

White House spokesman Josh Earnest said last week said that threats of a shutdown won't keep Obama from taking action.