Outsourcing outside the U.S. for federal contracts is typically illegal unless explicitly allowed by the Contracting Office most times, especially for defense work where all contractors must be U.S. citizens. Exceedingly rarely do federal agencies allow outsourcing outside of the U.S., both for security and political reasons. This mostly applies to services, but some products are also affected. The biggest exception to this, at times, is in the case of Overseas Contingency Operations such as in a warzone or other hostile areas where local contractors and companies might be used.

However, there have been instances that bypass this in a sort of "gray area". For example, I knew a company that was outbid on a job by over $200k to convert 11,000 documents to web pages and re-design an entire series of agency websites. The government themselves acknowledged it would take about 3 full time people (developers) 9-12 months to do the work, but the winning bid for the whole thing was from an outsourcer who bid less than $60k total. The agency in question turned a blind eye to the minimum wage requirements for technical labor categories written directly into the contract. Had this been a larger procurement with more money at stake, it would have easily been overturned and resulted in legal action against both the agency and the winning bidder (the outsourcer).

There is also the whole "buy American" thing written into most contracts nowadays, but which mostly applies to construction.