If you want to go by the NEC, you have to understand the difference between designing a branch circuit (panel to outlet) and an extension cord.
What you really need to take into account is the maximum current draw in Amps, and the welder's duty cycle.
As an example, if you have a welder that draws a maximum of 40A with a duty cycle of 50%, you would use the multiplication factor of .71 (from NEC Table 630.11). The calculated current draw, taking into account the duty cycle, is: 40A x .71 = 28.40A. From Table 310.15(B)(16) - a 10 gage conductor has an ampacity of 35 Amps at 75F.
Therefore, for the imaginary welder drawing 40A with a 50% duty cycle - a 10 gage extension cable would be adequate.