This may have been as close as a whole state has come to disobeying the Supreme Court. ThinkProgress explains what happens here:
Rep. Mark Pody (R) and Sen. Mae Beavers (R) originally filed their “Tennessee Natural Marriage Defense Act” back in September, introducing it at a “religious liberty” rally. HB 1412/SB 1437 dictates that “natural marriage between one (1) man and (1) woman as recognized by the people of Tennessee” would “remain the law in Tennessee, regardless of any court decision to the contrary. Any court decision purporting to strike down natural marriage, including Obergefell v. Hodges, is unauthoritative, void, and of no effect.”
The legislation lays out the lawmakers’ anti-gay biases — in particular, by comparing Obergefell to other decisions. According to the bill, the “United States Supreme Court is not infallible and has issued lawless decisions which are repulsive to the Constitution and natural law, including [Dred] Scott v. Sandford; Buck v. Bell; Korematsu v. United States; Roe v. Wade; and most recently, Obergefell v. Hodges.” These were decisions upholding slavery, the sterilization of people with intellectual disabilities, the internment of Japanese Americans, and a woman’s right to an abortion, respectively.
The bill would have had serious consequences for Tennessee, in the form of financial penalties from the federal government for deliberately disobeying federal law:
Passing the law could cost Tennessee more than $8.5 billion, according to the bill’s fiscal noteproduced by the General Assembly’s Fiscal Review Committee. This sum would largely come in the form of federal funding that would be cut for the state’s health care program (TennCare), the Supplemental Nutrition Assistance Program (SNAP), and Temporary Assistance for Needy Families (TANF).
Thankfully, a House panel had more sense:
A state legislative committee on Wednesday killed a bill that attempted to block same-sex marriage in Tennessee.
The bill failed in the House Civil Justice subcommittee on an unrecorded voice vote in which there were more "no" votes than "yes" votes to advance the bill. After the vote, the bill's sponsor, Rep. Mark Pody (R-Lebanon), said the bill is dead.
This is not a big win. It’s not a good sign that this bill could even be considered.