Norris was first elected to represent District 32 in the Tennessee Senate in 2000. The District is composed ofDyer, Lauderdale, and Tipton counties, and the eastern and northeastern portion of Shelby County. While in the Senate Norris was an active member in the American Legislative Exchange Council, having attended meetings of the organization. In 2002, Norris ran to represent Tennessee's 7th congressional district in the United States House of Representatives, but lost the primary to Marsha Blackburn. He was elected the State Senate Majority Leader in 2007. In 2015, Norris opposed a proposal to make the Bible the official state book. Norris ran unopposed for re-election in 2016, collecting $655,000 in campaign contributions, the largest among all Tennessee General Assembly candidates. Norris engaged in an effort to bar refugee resettlement in Tennessee and was a lead figure supporting a lawsuit challenging the constitutionality of the U.S. Refugee Resettlement Program. Norris created an online petition against refugee resettlement under the headline "Don't let potential terrorists come to Tennessee." Norris also supported the Trump travel bans. Norris resigned from the state senate on November 1, 2018, after being confirmed to the district court.
Federal judicial service
On July 13, 2017, President Trump nominated Norris to the United States District Court for the Western District of Tennessee, to the seat vacated by Judge J. Daniel Breen, who took senior status on March 18, 2017. Prior to his nomination, Norris was publicly considering a candidacy for Governor of Tennessee in 2018. Trump's nomination of Norris was supported by Republican Senators Lamar Alexander and Bob Corker of Tennessee. Norris' nomination was criticized by former U.S. District JudgeShira Scheindlin, an appointee of Bill Clinton, who wrote a New York Times opinion editorial in which she described Norris as one of a number of "the least qualified and most bizarre" of Trump's judicial appointments. On November 1, 2017, a hearing on his nomination was held before the Senate Judiciary Committee. During the hearing, Norris said in response to a question from Senator Amy Klobuchar that he viewed the case Obergefell v. Hodges as settled law. On December 7, 2017, his nomination was reported out of committee by a party line 11–9 vote. On January 3, 2018, his nomination was returned to the President under Rule XXXI, Paragraph 6 of the United States Senate. On January 5, 2018, President Donald Trump announced his intent to renominate Norris to a federal judgeship. On January 8, 2018, his renomination was sent to the Senate. On January 18, 2018, his nomination was reported out of committee by a party line 11–10 vote. In January 2018, Norris said he was unsure if he would be confirmed to the judgeship by the U.S. Senate and planned to remain in the state legislature until his nomination was ultimately confirmed. On October 11, 2018, his nomination was confirmed by a 51–44 vote. He received his judicial commission on November 8, 2018.
