The U.S. President has more power than one would guess (at least for the ignorant foreigner in me). It reminds me of the previous Finnish presidents, that in order to appease the Soviet union, they would sack the goverment because of not having a policy that was pro-soviet enough. New referendums were of course held, but a more Soviet-appeasing goverment was elected, since voting otherwise would be redundant.
Since the fall of the Iron Curtain, things have changed, and a lot of power has been shifted from the President to the Parliament.