This newspaper article says that New Hampshire Governor Chris Sununu expressed his opposition to moving the non-presidential primary from September to June. The bill to do that, HB 98, has passed the House but not the Senate.

The bill would make deadlines for minor party and independent candidates earlier. Currently independents, and the nominees of unqualified parties, must submit a declaration of candidacy in June, and petitions are due in August. The bill to move the primary, HB 98, would move them to earlier dates.