One vacancy from each party will be filled in the January 9 special general elections
He had called for Menendez to resign Friday, shortly after the long-time New Jersey Senator was indicted
Tuesday's races include a contest in an evenly-divided Pennsylvania State House.
The Democratic lawmaker had been diagnosed with Parkinson's earlier this year and is now facing a more severe version of the disease
The special election includes parts of Nashville, so some voters will participate in both.