Democrat Sen. John Arthur Smith, often described as one of New Mexico's most influential lawmakers, made the formal request for lawmakers to reconvene this summer in a letter to Gov. Susana Martinez.
The governor's office did not immediately respond to a request for comment made by the Associated Press.
Smith is chairman of the Senate Finance Committee, which helps craft the state budget. He and others warned during the legislative session earlier this year that continued slumping revenues could force lawmakers to revisit the budget.
Estimates released this week by legislative analysts show revenues for the fiscal year that just ended at $5.7 billion, or $159 million shy of expectations.