Buck odds = seize chances?

No. To "buck the odds" doesn't mean to seize chances, it simply means to persist despite the conventional wisdom that you'll fail, and is almost always linked to a claim that someone has succeeded despite the predictions of failure. In this context, it appears that Mr. Obama is attempting to seize the main chance, but we only have the author's word for that.

"The odds" refers to the odds of winning that someone would offer you if you were making a wager. Therefore, to "buck the odds" means to go against the conventional wisdom. So, if someone offering bets on a horse race says "that horse can't win," and offers high odds against that horse winning, to bet on that horse would be a case of bucking the odds. Of course, in real life there is no reason to assume that bucking the odds will be successful. But, as a figure of speech, it is almost always used to describe a case in which someone succeeded despite the odds against success.

To buck the odds means to attempt a task or tasks when you know the odds against success are high.

I made an error in the above; to buck the odds means to win even though the chances of success were perceived to be low at the time of making the attempt.

Good correction there. To buck the odds means you succeed against the odds, to succeed in a situation where it seemed more likely that you would fail.