By some accounts, Napoleon started with 500.000-600.000 men in June 1812, yet by the beginning of September (just before the first major setpiece battle at Borodino) this number had dwindled to under 200.000 - and this was before the winter had even set in. Had Napoleon attacked earlier, this still would have happened, and even with the Russians occupied elsewhere I doubt an ever-shrinking pool of 200.000 men could have forced the Russians to submit.
Then again, all this is largely ignoring the psychological aspects of a Napoleonic invasion while Russia was occupied elsewhere. Although in hindsight it seems to us that the French invasion was doomed to logistical failure, I highly doubt that the Russians had the same level of information at their disposal. Therefore, even while the Russians carried out their scorched earth policy, I'm sure they weren't 100% confident that this would be enough to see off the threat. Faced with the uncertainties of a two-front war, with one of the sides fielding a super army of half a million men, maybe they would in fact opt for an early (unfavorable) settlement after all.