If the Obama administration gets its way in revamping U.S. manned space-exploration efforts, two of the National Aeronautics and Space Administration's largest contractors could be on the hook for hundreds of millions of dollars in program-shutdown costs.

Lockheed Martin Corp. and Alliant Techsystems Inc. are waging a behind-the-scenes dispute with NASA's leadership over who will cover possibly more than $1 billion in such expenses, according to people familiar with the situation. The controversy has raised the financial and...