The Senate Rules Committee meets Saturday to continue considering whether Skandera should remain as head of the Public Education Department. She's held the job since Martinez took office in 2011.
On Friday, Skandera drew opposition from educational unions and others who said she didn't meet a constitutional requirement for an education secretary to be a "qualified, experienced educator."
Skandera's defenders, including some business leaders, said she has broad experience in educational policy although she's never worked as a public school teacher.
The Senate last rejected a cabinet secretary in 1997, when Republican Gov. Gary Johnson was in office.