What Alan_Hepburn stated is true. To simplify things, you want a compressor in which the "cut in" pressure is greater than the maximum pressure you want to put in your tires, or else you will be faced with the problem you experienced.
Since that number isn't always stated in the specs, a good rule of thumb is that the cut in pressure is usually 20-25 psi less than the cut out pressure (maximum psi). Plus you want to maintain a pressure differential from the tank to the tire as there will be pressure loss through the air hose & chuck.
So taking your 100 psi desired number, adding 25 psi for additional cut-in pressure plus another 10 psi for tank/tire differential, I'd recommend looking for an air compressor with a maximum psi rating of at least 135 psi. 150 psi would be even better.
Once you have sufficient pressure, than you can shop by the volume ratings CFM (or SCFM). The higher the SCFM number, the faster the compressor will be able to fill your tire at a given pressure.
My 5 hp 30 gal. home compressor with it's 110 psi max/90 psi cut-in would not fill my motorhome tires through the length of air hose I needed to use. IT had PLENTY of volume (SCFM) but didn't have the pressure to push the air from the tank into the tires. I bought a smaller Husky model with a 135 psi max. that I can bring to each tire and it works fine. I air them up to the max of 110 psi for the winter, then reduce to the proper pressure in the spring when we put the RV back in service. The compressor fits nicely into a storage bay.
I also use this compressor to blow out the air lines for winterizing. (I only use the pink stuff down the drains and the commode.) Because of this, I chose an oilless compressor as I didn't want it spraying oil into my water system. Something to think about if you're going to use this compressor to winterize as well.
You should be able to find a suitable 120VAC compressor which meets your needs for somewhere in the $100-$125 price range.
Good Luck,
~Rick