Government typically has a whole ton of contractors, sometimes twice the number of FTEs, but a cursory Google indicates NASA has only about 1000 contractors. Interesting, but the contract money probably goes to acquisition and commercial partnerships (https://www.osbp.nasa.gov/docs/top20_2020_contractors-TAGGED...).

That said, their FY22 budget is “only” $30B, which is less than Elon just paid for all of Twitter. This number usually surprises people but a lot of other space-related work is within the USAF and NRO budgets.

About a decade ago I was working on websites for NASA and just the contractor I worked for had over a thousand contractors. They were far from the largest, too.