Prosecutors said the officer was in regular contact with Tarrio regarding the activities of the right-wing Proud Boys in D.C. from July 2019 until at least January 2021.
Trump referred to what was taking place as "election interference."
Menendez has represented New Jersey in the Senate since 2006, while Kim was elected to the House in 2018.
The April survey shows Trump improving considerably over the results of the same poll's November results.
His potential move to move the case to federal court would follow a similar strategy from his former chief of staff, Mark Meadows, who has also sought to move his case.
Trump's reference to the "boxes hoax" appears to refer the FBI's seizure of materials from his Mar-a-Lago estate in August of last year.