Washington ? It looks like perfect political symmetry — party-line voting in Congress on the first key pieces of Barack Obama’s agenda, matching a deep partisan divide within the electorate in judging his performance as president.

But, for reasons that require a little explanation, it may be wrong to conclude from this evidence, as many are doing, that the center has fallen out of American politics and Obama is on a fool’s errand if he continues to pursue bipartisan support.

First, the data that shouts that I am wrong. No vote is more important in encapsulating the approach of the two parties to the basic issues of governing than the vote on the budget resolution for the year. It defines the spending priorities and the tax limits, along with many of the policy innovations that will be fleshed out in later legislation.

This year, not a single Republican in the House or Senate voted for the Democratic budget resolution and not a single Democrat endorsed the Republican substitute.

The Republicans denounced the deficit-spending envisaged by the Obama-endorsed budget and decried the Democrats’ habit of voting down every Republican amendment, as if none of the GOP ideas could possibly have any merit.

Democrats, for their part, called Republicans “the party of no,” pointing out that the GOP members of Congress had been almost as unanimously negative in their reactions to Obama’s stimulus bill and the catch-up budget left over from last year’s partisan gridlock.

As for the voters, the Pew Research Center reported earlier this month on a survey that showed the partisan gap in Obama’s job approval scores is the widest in contemporary history. He rated a thumbs-up from 88 percent of the Democrats and only 27 percent of the Republicans in the poll — a gap of 61 points.

At a comparable point in their first terms, the gaps for George W. Bush and Bill Clinton were only 51 and 45 points, respectively. A separate Pew poll found that since January, the percentage of voters who think that Democrats and Republicans in Washington are bickering more than usual has grown by 14 points, with a similar trend on the question of whether the country is more politically divided than in the past. By large margins, majorities now answer “yes” to both questions.

All this suggests the notion that Obama’s election marked a change for the better in the political environment was as fanciful as Michigan State’s chances against the mighty North Carolina Tar Heels.

But, still, this analysis ignores several potent factors, starting with the fact that the fastest growing portion of the electorate consists of people who have no strong partisan allegiance. These political independents are now as numerous as self-identified Republicans and are closing the gap on the Democrats.

Though badly underrepresented in Congress, where districting rules and campaign finance practices reinforce the two-party hegemony, the independent voters make up the swing vote in almost every contested election — including the presidential race.

It is the reaction of those swing voters — or the politicians’ anticipation of their shifting opinion — that drives the outcome of the big policy debates. You’ve had an example of this already with Obama’s cap-and-trade proposal for protecting the environment from carbon discharges.

Once political independents, who like the idea of clean air, grasped that cap-and-trade would mean a big tax increase for them, Republican opposition was reinforced and Democratic support weakened to the point that the Obama plan may already be doomed this year.

The crucial role of the independents will be demonstrated again and again when Congress takes up Obama’s challenge to reform health care, immigration and other broken systems, or renew arms control agreements. Because those independents are impressed when measures find prominent supporters in both parties, it will continue to behoove Obama to woo Republican help — no matter how tough the odds.

Presidents who hope to achieve great things cannot for long rely on using their congressional majorities to muscle things through. That is why a strategy based on the early roll calls and polls is likely to fail.