The French Fifth Republic and its occasional periods of “cohabitation” sheds some interesting light on the problems that arise in a period of divided government in the United States. The way the French system works is that the president needs to appoint a prime minister and a cabinet that enjoys the confidence of a majority in Parliament. By convention, when the president’s own party has the parliamentary majority, he essentially runs the show with the prime minister as his principle deputy and the cabinet doing cabinet stuff. But it used to be the case that parliamentary elections happened at minimum once every five years and presidential elections happened once every seven, so it wasn’t all that rare for the opposition party to gain the majority in the National Assembly. When that happens, the president needs to make the leader of the opposition the prime minister.
In practice, the resulting situation seems pretty similar to our divided government. But there’s a very important difference. The president can fire the prime minister, dissolve parliament, and call a new election. This, in practice, has made a world of difference during cohabitation periods. The upshot is that instead of the prime minister and the president constantly deadlocking, the prime minister basically just governs (on domestic matters). But he needs to be constantly worried about overreach. He could try to enact sweeping, super-controversial measures that the president opposes, but he’d be running the risk of being dismissed and losing the election. So he legislates with a much freer hand than John Boehner has, but he’s also in practice much more restrained.
Bringing this back to the United States, you can see that Barack Obama would clearly have a winning hand in the Fifth Republic framework. Even as a bleak objective situation has pulled his poll numbers down, he very consistently polls better than his congressional antagonists and he consistently takes negotiating positions that have more support than his opponents’ stands. This is clearly supposed to spook congressional Republicans and cause them to lose their spine. But unlike in the French case, it doesn’t actually provide him with any concrete leverage. He can’t call a snap election and get rid of Boehner. He can’t threaten to call a snap election and scare Boehner. Of course, unpopular stands can cost Republicans seats in November 2012. But the Treasury is running out of money in August 2011. By the time of Election Day, there will either be a Big Happy Bipartisan Deal of some kind or else we’ll all be spending large denomination platinum coins. And once there’s a deal, it’s at least plausible that all the prior negotiating positions become politically irrelevant.