Obama to make GOP rift much worse: Senator Thune

President Barack Obama's planned executive action on immigration is a "big mistake" that will make working with the GOP on other issues more difficult, Sen. John Thune told CNBC on Thursday.

"The president ought to work with the Congress, instead of against the Congress," the chairman of the Senate Republican Conference said in a "Squawk Box" interview.

The president on Thursday night is scheduled to announce plans that would lay the groundwork to protect millions of undocumented immigrants from deportation.

Read More Immigration takes Obama into risky political territory: Poll

Questioning the legality and constitutionality of Obama's approach, Thune said Republicans also "disagree in a very aggressive way" with the substance of how the White House wants to handle immigration policy.

The South Dakota senator said the problems that lead to illegal immigration, such as porous borders, need to be solved first. Then "there is probably a way in which we can address people who are here in this country illegally."

President Barack Obama speaking at the White House, November 5, 2014.
Reuters
President Barack Obama speaking at the White House, November 5, 2014.

Obama is about to draw an immigration line in the sand before the new Congress convenes next year and Republicans take control of the Senate. They won the majority in the midterm election earlier this month, which also saw the GOP add to its majority in the House.

A new NBC News-Wall Street Journal poll showed only 38 percent of Americans support executive action by the president on immigration without approval from Congress.

But 57 percent of those surveyed favor the creation of a pathway that would allow people in the U.S. illegally to eventually become citizens. That number jumps to 74 percent with the qualification that they pay fines and back taxes as well as undergo security background checks.

Read MoreImmigration a risk for Obama: NBC-WSJ poll

While opposing citizenship for illegal immigrants, Thune said, "There's probably a way you could get legal status. But the way to do it is not by executive action. We need to do this through the Congress, through the political process."

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