On January 14, the SAM Party of New York filed a lawsuit against the new law that removes parties from the ballot if they fail to poll at least 130,000 votes for President, or 2% of the presidential vote, whichever is greater. The new law went into effect last year even though the legislature did not pass any bill on this subject. It became law because the legislature empowered a new Commission to write new election laws. Here is the Complaint.
The case is SAM Party v Cuomo, s.d., 1:20cv-323. UDATE: it is assigned to Judge Lewis A. Kaplan, a Clinton appointee. It points out that the SAM Party does not desire to nominate anyone for president in 2020. It therefore seeks a ruling that requiring a party to run someone for president in order to retain qualified status violates the U.S. Constitution. The only other states that absolutely require parties to make a certain showing for president, to remain on the ballot, are Arkansas, Iowa, Kentucky, and Washington. Also Tennessee requires a showing for president in years when no U.S. Senate race is on the ballot. New Mexico law is ambiguous.
Most parties that are ballot-qualified in even a single state tend to want to run someone for president, so no lawsuit like this has ever before been filed.
The new law provides that if any part of it is held unconstitutional, then all of it is void. Thanks to Joe Burns for the news.