New Mexico Representative Bill Pratt (D-Albuquerque) has introduced HB 468. It lowers the number of signatures for almost all types of candidates, whether they are running in primaries, or they are the nominees of qualified minor parties, or whether they are independent candidates.
All would need 1,000 signatures if they are running for statewide office, and 500 if running for U.S. House, and lesser amounts for other offices.
There are two ways in which this bill would make ballot access more difficult, though. It would require the presidential nominees of qualified minor parties to submit a petition; currently they do not need a petition. Also it would increase the number of signatures needed for a member of a small party that is entitled to its own primary, to get on the primary. Thanks to Bob Perls for this news.