If certain Democratic incumbents, say, wanted to be able to refute "Big Government" or Government Motors labels, that would help, wouldn't it? I.e., "Who, us? Socialists who want the federal government to run a major industrial enterprise? Perish the thought."
On the other hand, maybe the timing really is a coincidence. You could argue that politically, the Obama Administration would rather not remind people of the federal government's role as No. 1 GM shareholder.
I could see that cutting both ways. The anti-Big Government diehards aren't going to vote for the Democrats anyway, so maybe there's no harm in reminding people that bailing out GM really did save an awful lot of jobs. At least one candidate in Michigan is doing just that, according to press reports. At the same time, you could spin today's IPO news as evidence that the government isn't holding GM any longer than necessary.
Of course, if you really wanted to get technical about it, you could say it was the lame-duck Bush Administration that bailed out the auto industry, at least initially. However, the political climate today doesn't really lend itself to complicated arguments -- it's more a time for what Mad magazine called "Snappy Answers to Stupid Questions."
Incidentally, the Treasury Department a couple of weeks ago updated a statement about the impending GM IPO with a reminder that Treasury wants to "exit" its investment in GM "as soon as practicable."
Treasury also said it wants to "maximize taxpayer returns," and to make sure that ordinary private investors have a chance to buy shares, not just big, institutional investors. The Treasury statement also mentions follow-on offerings.
It's widely expected that GM won't sell all its stock at once. However, it seems to be emerging as a priority that the initial move will be to get government ownership in the minority. That's a logical move, but logic doesn't always rule in politics.