A high-ranking GOP lawmaker on Sunday predicted his party won’t take the “bait” to shut down the government should President Obama take unilateral action on immigration reform.

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“I think (Obama’s) trying to bait us into doing some of these things - I don’t think we will,” former National Republican Congressional Committee Chairman Tom Cole (R-Okla.) said on ABC News “This Week.”

Noting that the president could have taken action when Democrats were in control of the Congress and White House, Cole charged that the president is “being political and cynical” with his anticipated unilateral action on immigration reform.

Asked why Obama couldn’t wait until the new Congress - with a GOP majority in both chambers - is sworn in in January, one of the lead Democratic lawmakers pressing for immigration reform action said that the party has waited long enough.

“I (am) … sick of seeing U.S. service members called up ... at the same time they receive their deployment notice … receiving a notice that their wife will be deported,” Rep. Luis GutierrezLuis Vicente GutierrezDemocrats rally behind incumbents as Lipinski takes liberal fire Dem leader says party can include abortion opponents DHS to make migrants wait in Mexico while asylum claims processed MORE (D-Ill.) said on “This Week.”

Gutierrez pointed out that Speaker John BoehnerJohn Andrew BoehnerIs Congress retrievable? Boehner reveals portrait done by George W. Bush Meadows to be replaced by Biggs as Freedom Caucus leader MORE (R-Ohio) said last week that "this is a fight that he's going to have with the president." "He's wrong," Gutierrez said. "He's going to have this fight with millions of Americans."

Cole cut off his Democratic colleague, "this fight is not over immigration, this fight is with the process that the president's choosing - a process that the president himself said was unconstitutional a couple of years ago." 

The GOP lawmaker ruled out a government shutdown as the proper response to any impending executive order, however.

“Absolutely not,” Cole responded when pressed if Republicans should use that tool in retaliation.

He also predicted that Congress could move pieces of immigration reform such as a border security bill, but did not offer a timeline.

--This report was updated at 11:40 a.m.