On March 29, the Green Party and the Constitution Party jointly filed a lawsuit in U.S. District Court, alleging that the New Mexico deadline for petitions to qualify a party is too early. That deadline is the first Tuesday of April, which this year is April 3. Here is the complaint. The case is Constitution Party of New Mexico v Duran.
In New Mexico, newly-qualifying parties nominate by convention, not by primary, so there seems to be no election-administration reason for the deadline to be so early. In the past, the deadline for a new party to qualify in New Mexico has been in October, then September, and then July. In 1995 it was moved to April, apparently because the majority party in the legislature, the Democratic Party, was angry that in the 1994 gubernatorial election, the Green Party gubernatorial candidate had polled 10.3% and apparently caused the defeat of the Democratic Party nominee. So, in 1995, the legislature made several hostile changes to the election law relating to minor parties, including moving the petition deadline from July to April, and also doubling the number of signatures needed for non-presidential minor party nominees to get on the November ballot.