The Senate Rules Committee heard more public testimony on Saturday about Skandera, who's been in charge of the Public Education Department since Martinez took office in 2011.
Skandera drew opposition from educational unions at Friday's hearing, and teachers turned out in large numbers Saturday. Opponents say Skandera doesn't meet a constitutional requirement for an education secretary to be a "qualified, experienced educator."
Skandera's defenders, including some business leaders, say 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.