Hebert, a former alcohol commissioner and state lawmaker running without party affiliation, filed a lawsuit challenging the criteria that excluded him from the debate being held by Louisiana Public Broadcasting and the Council for A Better Louisiana.
A two-day hearing on Hebert's injunction request is expected to wrap up Thursday with a ruling from Judge Tim Kelley. Hebert, who is not a lawyer, has been representing himself in court.
Only five of the 24 Senate candidates met the debate criteria, which required participants to have raised at least $1 million and polled at 5 percent support. Hebert is not fundraising for his campaign.