Well, he’s back. Now that the big question of the day has been answered, it’s time to think about whether Barack Obama’s second term is likely to be any more harmonious than his first. Will it be plagued by the same legislative gridlock that has characterised the last two years, or will the President find himself with a more co-operative Congress?

Like our federal Parliament (which was modelled after it), the US Congress consists of a House of Representatives based on population and a Senate based on equal representation of states. At the 2010 mid-term elections the Republicans won a solid majority in the House but failed to take control of the Senate. Although today’s results are still incomplete, we already know that this state of affairs is going to continue.

Let’s look at the House first. Large shifts in House numbers are rare; its 435 members tend to entrench themselves by relentless pork barreling and ingenious drawing of boundaries. After a generation of Democrat control, the Republicans won the House (and the Senate) in 1994, losing it again in 2006 before winning it back four years later. All three of those swings were mid-term elections; in presidential election years the status quo generally prevails. Even when Ronald Reagan won a 49-state landslide in 1984, the House stayed with the Democrats.

As of 3.15pm AEDT (11.15pm in New York), all the networks have projected that the Republicans have held the House comfortably. MSNBC, for example, is saying 238 to 197, a net loss of just four seats for the Republicans compared to last time. It will be tomorrow morning (Australian time) before we will have a complete picture, but there’s no doubt that Obama will still have a hostile House of Representatives.

The Senate is rather more interesting. Like its Australian counterpart it has staggered six-year terms, but because elections happen every two years, only a third of senators at a time face re-election. The seats being decided today were last voted on in 2006, an abnormally good year for the Democrats, so they have much more to lose: although their overall majority is only 53-47, among the 33 seats at stake that figure is 23-10. (There are two independents, one of whom is retiring, who caucus with the Democrats, so I am counting them in the Democrat total.)

So the Republicans approached the Senate this time with high hopes, which have been progressively dashed in recent months. Perhaps the most spectacular was Indiana, where Tea Party Republicans ejected their own incumbent, Richard Lugar, in the Republican primary for having supported arms control, and instead endorsed Richard Mourdock, who spent the last week of the campaign trying to explain his opposition to legal abortion for r-pe victims, having said that pregnancy due to r-pe was “a gift from God”.

Sure enough, Mourdock went down to a relatively unknown Democrat challenger, Joe Donnelly. That was the third GOP loss for the day: Scott Brown, who had won a by-election in 2010 to take Teddy Kennedy’s old Massachusetts seat, was beaten by Democrat Elizabeth Warren, while the Maine seat formerly held by moderate Republican Olympia Snowe, who is retiring, has fallen as expected to an independent, Angus King, who is likely to caucus with the Democrats.

That brings the Republican starting point back to 44. In addition, there are three likely Republican gains: Nebraska, North Dakota and Montana, although the last of those is looking a bit shaky. But that still only brings them back to 47. Another two threatened Democrats have held on. Tim Kaine managed a narrow victory in Virginia to fill the seat of the retiring Jim Webb, and incumbent Claire McCaskill scored more convincingly against Republican challenger Todd Akin — another who had trouble with his views about r-pe.

That leaves a minimum of 50 Democrats plus two sympathetic independents. If, as seems likely, they also hold New Mexico, the overall numbers would be unchanged — and there is still the possibility of an upset Democrat win in Montana or Nevada. So the President will still have one friendly chamber, although the filibuster rules still give Republicans a lot of power there. Divided government will continue at least for another two years, until Democrats get another crack at the House in 2014.

Which all adds up to a very good election for the opinion polls, and for the pundits who relied on them. Perhaps the most famous of the latter, Nate Silver at FiveThirtyEight, looks like being spot on for the Senate (Indiana and Montana were the only two he had even been calling competitive), just as he is yet to get a single state wrong for the presidential ballot — although Virginia is still line-ball as I write. The moral is, given a choice, always go with the hard data.