WASHINGTON — Call it the Party-of-Government Paradox: If the nation’s capital looks dysfunctional, it will come back to hurt President Obama and the Democrats, even if the Republicans are primarily responsible for the dysfunction.

Then there is the Bipartisanship Paradox: No matter how far the president bends over backward to appeal to or appease the Republicans — no matter how nice, conciliatory, friendly or reasonable he tries to be — voters will judge him according to the results. And the evidence since 2009 is that accommodation won’t get Obama much anyway.

This creates the Election Paradox: Up to a point, Republicans in Congress can afford to let their own ratings fall well below the president’s, as long as they drag him further into negative territory. If the president’s ratings are poor next year, Democrats won’t be able to defeat enough Republicans to take back the House and hold the Senate. The GOP can win if the mood is terribly negative toward Washington because voters see Obama as the man in charge.

Everything the Republicans are doing makes sense in light of the three paradoxes, even though, by the numbers, they have been the big losers from the summer’s debt ceiling fiasco and their broader refusal to cooperate with Obama.

A Pew Research Center survey released last week showed Obama with a 49 percent disapproval rating, but Congress with a 70 percent unfavorable rating. So Obama is still “ahead.” The Democrats are also better regarded than the Republicans — or, perhaps more accurately, less poorly regarded. “Only” 50 percent of respondents had an unfavorable view of the Democratic Party; 59 percent had an unfavorable view of the Republican Party.

But the trend on the president’s numbers has been downward, and the Republicans seem willing to pay a high price to keep them moving that way. Remember: The core GOP argument is that government can’t do much good and generally makes everyone’s life worse. Democrats are the ones who insist that government can solve problems and improve people’s lives. If government isn’t doing that — if it is discredited and made to look foolish — guess whose side of the debate is weakened?

Obama’s central task is to break out of the three paradoxes, not just to get re-elected but also to get anything done. Having tried conciliation, his only alternative is to build pressure on the Republicans. He needs to get them to act, or, failing that, to make clear who is responsible for Washington’s paralysis.

That’s why his coming speech on jobs has to describe a program that’s broad and imaginative enough to capture the public’s attention. The middle-of-the-road voters his advisers want to win back look first for chief executives to be strong, decisive, and principled, not at how many millimeters they are from the political center.

Despite reports that the White House is split over how much Obama should ask Congress to do, the president has signaled that he understands the stakes. “My attitude is that my job is to present the best plans possible,” Obama said in an interview Tuesday with talk-show host Tom Joyner. “Congress needs to act. If Congress does not act, then I’m going to be going on the road and talking to folks, and this next election very well may end up being a referendum on whose vision of America is better.”

Obama hates to bring up the nasty fact that we have political parties, but very soon, he will have to point out that it is Republicans in Congress who are blocking his program. They will either have to start worrying about its low ratings, or begin to pay a real price for obstruction.

The model, of course, is Harry Truman. In a lovely book on the 1948 election, The Last Campaign, Zachary Karabell explains the problems that Truman’s attacks on the “do-nothing” Republican Congress created for his GOP opponent, Thomas E. Dewey.

“Dewey couldn’t distance himself too much from Congress or he would lose the support of his own party and perhaps jeopardize Republican chances in the congressional elections,” Karabell wrote. “Yet he needed to create some space between himself and the Congress in order to avoid being dragged down in their wake. It was a precarious position.” Indeed it was.

Truman, it’s true, didn’t get to this strategy until the election year. But the unemployment rate in 1948 averaged below 4 percent. Obama doesn’t have the luxury of waiting.

E.J. Dionne’s email address is ejdionne(at)washpost.com.

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