TEMPE, Ariz. — When Michael Crow became president of Arizona State University seven years ago, he promised to make it “The New American University,” with 100,000 students by 2020. It would break down the musty old boundaries between disciplines, encourage advanced research and entrepreneurship to drive the new economy, and draw in students from underserved sectors of the state.

He quickly made a name for himself, increasing enrollment by nearly a third to 67,000 students, luring big-name professors and starting interdisciplinary schools in areas like sustainability, projects with partners like the Mayo Clinic and Sichuan University in China, and dozens of new degree programs

But this year, Mr. Crow’s plans have crashed into new budget realities, raising questions about how many public research universities the nation needs and whether universities like Arizona State, in their drive to become prominent research institutions, have lost focus on their public mission to provide solid undergraduate education for state residents.

These days, the headlines about Arizona State describe its enormous cuts.

The university has eliminated more than 500 jobs, including deans, department chairmen and hundreds of teaching assistants. Last month, Mr. Crow announced that the university would close 48 programs, cap enrollment and move up the freshman application deadline by five months. Every employee, from Mr. Crow down, will have 10 to 15 unpaid furlough days this spring.