Historical results are definitely achievable in this game, and indeed it is possible to far outstrip the German timeline. Playing against normal AI, I have little difficulty most of the time achieving a victory by September/October. For a challenge, I play at hard or really hard. I find only the very highest difficulty level is actually unbeatable.
If you're not winning as the Germans against the AI, it's because you aren't playing to the full combination of your strengths. The game requires a skilled coordination of many different aspects - cards, air power and artillery, command bonuses, political points, unit posture, refitting, and tactical bonuses from surround, etc.
Some people seem to think that Barbarossa should simply be a matter of moving Germans forward, and watching Soviet defence lines crumble as soon as they are touched. In fact you have to plan encirclements very carefully - if you do, they can be executed and it isn't all that hard to encircle Soviet pockets of 10+ divisions, or even 30+ divisions sometimes. As was historically the case, you don't have a prayer unless you can pull off these encirclements.
I think maybe people also forget that the Germans had 700,000+ casualties by the end of 1941, and as early as Smolensk some divisions were reporting 50%+ losses (battle and mechanical failure) of AFVs. And that's with nearly "perfect play", in an operational if not strategic sense. I hate Eastern Front games where the Germans suffer next to no losses at all during 1941.
This game is not without its flaws. In particular, I find it is actually a bit skewed towards the Germans, particularly in AGS where it has some a-historical bonuses, for the Axis Allies in particular. And the game doesn't give the Russians enough incentive to fight hard for every scrap of ground - since only Leningrad, Moscow, and Rostov really matter, a Russian "three fortresses" strategy is viable, to the neglect of historically important parts of the front like Orel-Kharkov area.
The Soviet paralysis is well-simulated through inability to move units around as a player might like to, rather than through tactical penalties. If you can't play to the Russians' weaknesses in mobility and reaction speed, and insist on a tactical advantage, then you are misunderstanding the game and you will fail. If you can't figure out the logistics game, you will fail. If you can't work out how to load bonuses up on your schwerpunkt, you will fail...