If the midterm elections were held now, Republicans would likely take control of the House of the Representatives. It’s as hard these days to find a Democrat who’s not alarmed as it is to find a Cleveland Cavaliers fan who’s cheering for LeBron James.

Worse for Democrats: They face two very different challenges, and addressing one could make the other worse. The outcome of the 2010 elections thus depends in large part on whether they can find a solution to a set of simultaneous equations before November.

On the one hand, independent voters are turning on them. Democratic House candidates enjoyed a 51 percent to 43 percent advantage over the Republicans in 2008. This time, the polls show independents tilting Republican by substantial margins.

But Democrats are also suffering from a lack of enthusiasm among their own supporters. Poll after poll has shown that while Republicans are eager to cast ballots, many Democrats seem inclined to sit this election out.

The dilemma is that arguments that might motivate partisans could further alienate the less ideological independents. The classic formulation holds that the party can either move left to excite its base or move to the center to win back independents.

If there is an answer to this conundrum, it lies in the reality that many voters — partisans and independents alike — are not particularly ideological. They respond to facts as they see them (a stalled economic recovery) and to a party’s performance (the Senate Republicans’ obstruction ends up hurting Democrats because they are supposed to be in charge).

The GOP’s gridlock strategy was well thought out and has paid enormous dividends. Republican leaders understood that delay was their friend because the immediate elation over President Obama’s election was bound to wear off. And while Republicans erected their blockade, they insisted that all the nastiness arose from Obama’s failure to reach out to them.

The politics of passive-aggressiveness worked twice over. Independents hated all the fighting. And even when Democrats won on health care and other issues, they emerged less with a renewed sense of purpose than with feelings of exhaustion and frustration over all the compromises it took to eke out victory.

Turning all this around is a White House mission, and the president’s campaign stops last week in Missouri and Nevada previewed his effort to paint Republicans as both extreme and recalcitrant. His speech in Kansas City included one major innovation, an echo of a legendary 1940 assault by Franklin D. Roosevelt against his political opponents in Congress — “Martin, Barton and Fish.”

Obama went after the alliterative trio of “Barton and Boehner and Blunt,” references to Reps. Joe Barton of Texas, John Boehner of Ohio and Roy Blunt of Missouri. Challenging them for their resolute opposition to every Democratic approach, Obama asked “if that ‘no’ button is just stuck.”

He hopes that this Republican trinity can do double duty. It creates a tangible group of foes against whom Democrats can rally. And it reminds independents that a Republican vote this fall would not simply be a rebuke to Washington but also an affirmative ballot for Republican leaders who are none too popular themselves.

Democrats are counting on a similar twofer from their attacks on the current brand of Republicanism as being too doctrinaire and too extreme. The energy that the tea party provides Republicans could be offset by a negative reaction in the electoral middle to the new movement’s ferocity. This is the GOP’s simultaneous equation puzzle: It must benefit all it can from tea party organizing without getting tarred by its members’ frequently radical outbursts.

But there is an intangible: Passion counts in politics. It motivates a movement’s most fervent followers but can also carry along moderates attracted to those who promise change and profess great certainty about how to achieve it. Barack Obama got himself elected president by understanding this.

Passion may come especially hard to Democrats this year, and even in the best of times, it can be difficult to muster among liberals. As the philosopher Michael Walzer observed in his book “Politics and Passion,” liberals by their very nature highly prize skepticism, irony and doubt. Walzer argued that “administrators do well when they follow their rational convictions,” but “political activists must be more passionately engaged, or else they will lose every struggle for political power.”

On paper, Democrats have a rational solution to their political math problem. They must still find the passion that executing it will require.

E.J. Dionne’s e-mail address is ejdionne(at)washpost.com.