"What they fail to understand is that a higher gravity is needed. With the current gravity, warming the planet will result in a loss of atmosphere. With a higher temperature, the Boltzmann distribution of gas molecule speeds will have the high speed tail stretching well past escape velocity with the current gravity on Mars. "
Drop enough small asteroids on Mars, (and I'm talking a LOT of them!) and increase the mass while building up the gas pressure and temp, all at once... Of course, we probably ought to look the place over rather carefully first, as there isn't much that would survive the "rain" we caused. (Simplistic solutions for simplistic people...)
You are right, not much would survive adding sufficent mass to increase the gravity of Mars. Such mass would add hundreds of kilometers to the diameter of the planet. Nothing original would remain.
Of course if you increase the mass of the Moon, you will change the orbital characteristics (and climate, seasons, tides, etc.) of Earth. That's not a trade I want to make.
I don't think there's enough mass in all the asteroids, combined, to raise Mars' mass that much.
[ http://www.nineplanets.org/earth.html ] Earth mass: 5.972e24 kg
[ http://www.nineplanets.org/mars.html ] Mars mass: 6.4219e23 kg
Okay, now I'm 90 per cent sure.