Because relatively cheap GPS receiver clocks drift, typically 4 satellites are needed for a position. You can assume an elevation, especially at sea level, and solve a position with three satellites but this introduces other factors (ellipsoid vs geoid, satellite constellation geometry, etc) that can make a good position difficult to obtain.

In practice there are enough satellites that these considerations are theoretical. Most situations that would involve limited satellites also introduce stuff like multi path reflections that further degrade position accuracy.

In North America your GPS probably connects to between five and twelve satellites.