Ok, let's think this through.
First, the direct rainfall on the driveway. At an insane extreme of 3" per hour, that's around 560 gallons of rain in an hour. For a pump that's pushing 250 GPM, it's insignificant (under 4% of the pump's capacity).
Next, the other water sources. EVERYTHING should be graded away from the driveway. The roof, the lawn, EVERYTHING! So, the only source aside from rain to consider should be the street.
The sidewalk is effectively a weir, so this is easy to calculate. If the water at the street is 3/4" above your sidewalk, your 3" trash pump is doomed to be too small. Less than that, and perhaps it can keep up. Yep, a mere 3/4" of water cascading over that edge, and it's game over!
This is why I wrote what I wrote above. First, check the street storm drain grates. Obstructions can raise the street water level, and even a quarter inch may be all it takes. And second, sand bags around the driveway mouth should be plenty to allow a pump to keep up until the whole lawn is flooded and water finds another way to your foundation.