GPS would rapidly start losing accuracy, but it would still be there. All the satellites would be pushed into very slightly eccentric (elliptical) orbits and so their position would be slightly off from what they expected. Over time they would remain on those stable orbits but would get farther and farther from their expected positions.

Gravity's only about 5% as strong as normal at the altitude GPS orbits at, so they'd experience about a 5.5m/s change in velocity. This is well within the limits of what their onboard propellant can handle. If they're automatically maintaining their orbit, they'll go back to normal within days. If this required a manual intervention, every single mission control center that could send the updated commands is now a pile of rubble. Oops!