The mission and the the artificial intelligence is designed to cheat, at any and all costs, so you do not win. If you make it to the "Gun Running" mission, you have effectively completed the game. Congratulations.
Yes I also thought so, but I beat it after about 100 attempts. I figured it out as follows:
1) Go get the truck and get to the first gun shop to deliver goods, this will be already marked as soon as you get into the truck. You should have figured out by now that after you hit (X button) the car full of goons come after you. (instead of stopping in front of the gun shop at the T-intersection park your truck around the building to the right of the gun shop just far enough to where it still says X to sell guns. Hit (X button). After the you get control of Joe get out the truck and run north from the truck and there is an alley to your right. Hide in there and stay far enough back in there and keep peeking in and out around the corner and shoot all of the goons in the car, also cops will shoot at you. kill all the goons (4) and cops.
2) Once you have this (1/4) of the time should be gone, get back in the truck and head north towards the tracks, take a left on the tracks and head to the body shop. Quickly repair damage, supercharge the truck, and change the plate. Before you go to the next gun shop, go to your map and look South. There should be 2 gun shops close to each other. (To save time when in the tunnel going back to Joe's safe house crossover traffic and go down the on ramp), pass Joes apartment make a right at the stop sign, go down this street and make a left, but don't go down the road, go threw the trees and over the sidewalk to the 2nd gun shop.
3) After the second one is done go to the map and look to the East of the gun shop that you were just at, mark this on your way-point and head to it.
Finally get to the garage that is marked on the map, press (X button) when you see the letter P rotating. This should complete the mission, this was the easiest way for me to beat it.
(Note: After you kill all the goons at the 1st gun shop, there will be no more goons after you.)