It took me about 6 major tries, with a number of abortive attempts dying on the way to Vegas. My winning strategy went along the lines of tagging speech, guns, and...I forget. Maybe lockpick. 9 int, with an implant around level 4 (maybe I made it by 3...), going with Education and Comprehension ASAP. Arm yourself with a 9, or whatever's handy. You can fix up the SMG in Doc's house with a 2 point investment at level 2. Your first decent armor will be Combat Armor looted from Durable Dunn's. But combat should mostly be avoided in the beginning. You can do Primm if you're not afraid of hitting the hotel solo, or losing too many pre-implant skill points.
Take the very long way around to Vegas, passing through Nipton, Novac, etc. Pick up Veronica ASAP. She wrecks things, even with 1 charisma. Screw around Vegas long enough to do some easy, combat-light quests. Go back to Primm as soon as you have the parts or Repair to fix up ED-E. Enhanced sensors are awesome. So is having another (not-quite-warm) body between you and the enemy. Do Nellis early, because artillery kills you dead no matter how well armored you are. Or just skip Nellis entirely. I think you can do that with Yes Man. I didn't. I eventually figured a one-stop path through the barrage.
Also early on, once you've got the science/lockpick chops to do so, sneak into Repconn HQ, and loot the brotherhood guy to give to Veronica.
From there, I did a lot of easy peasy quests, got enough Repair for juryrigging, made a bazillion caps (Caravan can do the same basic thing), bought the best Combat Armor there was, and then proceeded along Yes Man's quests. House is really easy to kill as long as you don't try fighting securitrons. I was incredibly stupid and (very carefully) did Black Mountain for the brotherhood to get power armor. It would probably have been more effective to power along to the endgame, and do Auld Lang Syne.
Once you get to the endgame, it's just a matter of doing lots and lots of drugs. Having an AM Rifle helps too.