Nasa opens applications on an as-required basis.
For this window NASA hit social media hard to promote the openings, perhaps explaining the large number of resumes sent in.
"We have our work cut out for us with this many applications," said Brian Kelly, director of Flight Operations at Johnson Space Center in Houston.
"But it's heartening to know so many people recognize what a great opportunity this is to be part of NASA's exciting mission," he said.
Applicants for the Candidate Program must be citizens of the United States.
They must also have a bachelor's degree with a major study in an appropriate field of engineering, biological science, physical science, or mathematics
NASA said chosen candidates will go through about two years of initial training on spacecraft systems, spacewalking skills, teamwork, Russian language and other skills.
NASA said it will announce its selections in mid-2017.