The United States government currently claims 4 meter RMS (7.8 meter 95% Confidence Interval) horizontal accuracy for civilian (SPS) GPS. Vertical accuracy is worse. Mind you, that's the minimum. Some devices/locations reliably (95% of the time or better) can get 3 meter accuracy. For a technical document on that specification you can go here.
For more general GPS accuracy information, head to GPS.gov's website. That website also includes data and information on WAAS-enabled systems and accuracy levels depending on location. It's a great resource.
Basically, you can't get 2 meter accuracy reliably without some form of correction.
Edit: Something else to contemplate is using a device that can communicate with both GPS and GLONASS satellites. I'm not aware of any accuracy articles or studies that combine both systems to improve accuracy, but at the very least, it increases the potential satellites that may be available at one particular location/time, especially near the poles.