Sen. Lamar Alexander won Tennessee’s Republican primary Thursday, effectively ensuring he will get a third term in office and a chance to set the Senate’s agenda on labor issues if the GOP wins control of the chamber this fall.

Alexander has a shot at becoming chairman of the Senate Health, Education, Labor and Pensions Committee, as polls show Republicans have a better than even chance of taking back the Senate in November. That is likely to be a big frustration for Big Labor, since Alexander has consistently voted against its agenda.