The government is on the verge of selling some AIG (AIG) shares for the first time since its 2008 rescue of the insurer. Offering papers filed Wednesday show taxpayers should reap some $6 billion from the sale, which will take Treasury’s stake in AIG down to a piddling 77% from 92% now.

But the yearlong plunge in AIG’s stock price (see right) means a happy ending in this $182 billion saga is looking considerably less likely than it did just a few months ago.

The feds were on a roll as 2010 ended. First Treasury sold a big chunk of General Motors (GM), and then it cashed out of an even bigger bailout, Citigroup (C), at a $12 billion profit. This was unexpected, let’s say. Then another upside surprise came as AIG stock embarked on an unlikely year-end rally that took it briefly above $50 a share.

But that rally fizzled, and with it the hopes of an easy bailout from this bailout. With AIG shares trading Wednesday at $31 – down from a year ago, let alone from the recent highs — the government stands to sell shares not far above its breakeven point of $28.73.

A breakeven sale alone is not a big setback, obviously. Policymakers are less interested in making money on their share sales than in getting the government out of the bailout business as soon as possible. Any transaction that reduces Treasury’s stake by 200 million shares is a winner from that perspective.

But the plunge in AIG’s shares, even as U.S. stock market indexes close in on their bubble-era highs, could saddle the government with some unpalatable choices in the months and years ahead.

If AIG’s condition improves and its stock stays within hailing range of the breakeven point, the government can keep selling, even at small losses, and make the case that the operation has been a success. Few would have guessed two and a half years ago that there would be any chance of getting out of AIG whole, after all.

But if AIG takes further hits on its insurance operations – which seem to have been massively under-reserved during the supposedly halcyon Hank Greenberg era – or if its profits otherwise fail to bounce back, the stock could fall sharply even from here. And that could leave the government with two unpleasant options: Keep selling and let the losses (and the anti-bailout yelling) mount, or hold on and cross your fingers that the tide will turn.

And of course there is also the prospect that a frothy-looking stock market will itself turn lower. This probably would not be good news for an also-ran insurance company that is so desperate for income that it tried recently to buy back the securities that nearly bankrupted it in the first place.

Other things could happen, of course. Maybe there will be a massive stock market rally and AIG will return to the $50s. Perhaps the U.S. economy shake off its malaise and everyone’s growth outlook will get bumped up. Possibly the politicians will get their act together and end the worries about the U.S. spending picture.

But none of those outcomes look very likely, which is going to leave Treasury with 1.4 billion shares of a mediocre insurance company and a clock ticking more loudly by the day. Bailing out of a bailout, we’re finding this year, is not for the faint of heart.