The points above are worth considering. No fuel station in America will function if the power grid is out. No fuel station will work if its electronics are fried.
If they do work, well, the gasoline is delivered to them by tanker trucks. They won't work either. Neither will refineries...
Your generator will last as long as your own supply of gas lasts. That's it.
Worth noting too that no matter what Mad Max may lead you to believe, gasoline has a shelf life.
Learn about fuel storage, including how long fuel can be stored, the causes and effects of degradation, laws and regulations, and more.
axi-international.com
Stored well (in a sealed container, under minimal humidity, with a stabilizer) it'll maybe last a year. A part filled container with air at 60% humidity? Maybe 2-6 months...