The turning force at low speeds (below 70 to about 100 km/h) mostly comes from the so-called mechanical grip of the tyres themselves. At such low speeds the car can turn at 2.0 g. At 210 km/h (130 mph) already the lateral force is 3.0 g, as evidenced by the famous esses (turns 3 and 4) at the Suzuka circuit. Higher-speed corners such as Blanchimont (Circuit de Spa-Francorchamps) and Copse (Silverstone Circuit) are taken at above 5.0 g, and 6.0 g has been recorded at Suzuka's 130-R corner.[18] This contrasts with 1 g for the Enzo Ferrari, one of the best racing sports cars.
The large downforce allows an F1 car to corner at amazing speeds. As an example of the extreme cornering speeds; the Blanchimont and Eau Rouge corners at Spa-Francorchamps are taken flat-out at above 300 km/h (190 mph), whereas the race-spec touring cars can only do so at 150–160 km/h (note that lateral force increases with the square of the speed). A newer and perhaps even more extreme example is the Turn 8 at the Istanbul Park circuit, a 190° relatively tight 4-apex corner, in which the cars maintain speeds between 265 and 285 km/h (165 and 177 mph) (in 2006) and experience between 4.5 g and 5.5 g for 7 seconds—the longest sustained hard cornering in Formula 1
http://en.wikipedia.org/wiki/Formula_One_car
Adding ground effect or fan technology would increase available downforce a lot which would allow for much higher lateral g's.
I have been able to find very little information on how much side to side lateral g's a human body can withstand but i did find this.
Individual are more tolerant of forces received in the +/-Gx axis than of those received in the other axes because transverse Gs interfere very little with blood flow. Extreme values of transverse G (12 to 15 +/-G) acting for five seconds or more can displace organs or shift the heart’s position and, thereby, interfere with respiration.
http://www.cavalrypilot.com/fm1-301/ch4.htm
I am assuming that the high lateral G's are gradually achieved (1-3 seconds) rather than suddenly (0.1-0.3 seconds) as internal bruising and bleeding would be more likely in that situation.
Even disregarding driver safety i do not know how much further they could push F1 before they become totally impossible to drive.