Photo credit: Sarah Gilbert

Sen. Mark Warner is trying.

The Virginia Democrat, the prototypical political moderate, is part of a small group of senators seeking to do what nobody else in Washington seems capable of doing. They are trying to devise the Big Deal that will provide a fix to the country's frightening budget deficits, not just now but for years to come.

Make no mistake: This is the most important game in the nation's capital right now. Yet the odds of success aren't good. Doing the deal that Mr. Warner and friends envision will require a solid anchor in the political center—at precisely the time when the ranks of moderate centrists in Congress are the thinnest they've been in years.

Ultimately, that means it will fall to President Barack Obama to provide that anchor in the political center. So far it isn't clear he will—though a new study to be released later this week on the importance of moderate voters to Democrats' fortunes shows doing so actually could be a political winner for him and his party.

Here's the deal that's in the works: Mr. Warner is one of six senators—three Democrats, three Republicans—who are trying to put together legislation that would commit to law the cuts in federal deficits set by a commission Mr. Obama established last year to find a way to curb federal red ink.

The debt commission's final report said that making the deficit cuts it envisions requires three big things: cutting discretionary spending (House Republicans are showing the way on that right now); limiting the growth of entitlements (read Social Security, Medicare and Medicaid); and enacting a broad tax reform that would raise more revenue by simplifying the tax code and killing off deductions and credits while lowering rates overall.

That blueprint got the support of a majority of commission members, but not the number required to force Congress to vote on the blueprint. So Mr. Warner and friends are considering legislation that would, in effect, put the debt commission's plan into law. Its limits on spending and tax revenues would be set as legal targets; if Congress failed to pass legislation to meet them, across-the-board spending cuts and reductions in tax deductions would kick in automatically.

This grand idea faces two big obstacles. Democrats will be tempted to flee because their liberal base can't countenance the idea of reductions in Social Security, and Republicans will be tempted to flee because their conservative base will see a tax reform that raises more revenue as a violation of its no-tax-increases orthodoxy.

Ideally, proponents could resist those attacks by falling back on a strong bloc of political moderates in Congress. But the 2010 election hit the ranks of political moderates particularly hard.

In the Senate, for example, Democrat Evan Bayh and Republican George Voinovich, who likely would have been champions of such an effort, retired. Robert Bennett, a Utah Republican who had shown willingness to work across the aisle in this kind of effort, was defeated by a more conservative Republican. Blanche Lincoln of Arkansas, a Democratic moderate, was washed away by the GOP tide.

Which brings us back to the need for Mr. Obama to help hold the political center. To do so, he would have to cross swords with many in his party's liberal base.

Yet the rewards among moderate voters for Mr. Obama could be great, as shown in the new study done for The Third Way, a group that advances the views of moderate Democrats. The study, a look at the importance of moderate voters written by centrist Democrats William Galston and Elaine Kamarck, shows why Mr. Obama's re-election—and Democratic success in general—can't be built solely on the party's liberal base.

In 2008, liberals made up just 22% of the electorate, while conservatives comprised 34% and moderates 44%. The logic of the math is inescapable. Democrats can't win merely by satisfying their liberal base, which is too small and significantly smaller than the conservative base Republicans start with—a conservative base that likely has grown some since 2008. To win, Mr. Obama and other Democrats simply have to appeal to a large share of the nation's moderates.

Indeed, Mr. Galston and Ms. Kamarck write, "since 1980, no Democrat has been elected president without winning at least 60% of the moderate vote cast for the two major parties."

One of the characteristics of moderates, the two scholars note, is that they tend to look more favorably on deficit reduction than do liberals. The authors offer some ideas, including changes in primary elections and the drawing congressional districts, to build the power of moderate voters over time.

Right now, though, the budget debate offers Mr. Obama a chance to not only do right, but to do well politically in the process.