Obama's comments come near the end of the period in which the auto workers are voting on whether to join the UAW or not.
Local lawmakers including state Sen. Bo Watson (R) and Gov. Bill Haslam (R) have expressed opposition to the workers joining the UAW.
"Should the workers choose to be represented by the United Auto Workers, then I believe additional incentives for expansion will have a very tough time passing the Tennessee Senate," Watson recently said.
Additionally, Americans for Tax Reform President Grover Norquist and and the Center for Worker Freedom have rented twelve digital billboards in the Chattanooga area to call on the auto workers not to join the union.
This story was updated.