Thune, one of South Dakota's two Republican senators, said Feb. 3 he is "not in favor of federalizing elections."

The short-lived government shutdown ended with a new funding bill that did not include money for the U.S. Department of Homeland Security.

“I’m not in favor of federalizing elections, no. I think that’s a constitutional issue,” Thune told reporters Tuesday. “I’m a big believer in decentralized and distributed power. And I think it’s hard...