As New York Mayor Michael Bloomberg (I) and a bevy of moderate politicians from both major parties exchange ideas for reinvigorating the political center, they might consider whether the presidency — the office that has attracted most of the attention so far — is actually the most promising target for their efforts. Because of the steep hurdle posed by the Electoral College system, it might actually be a more effective strategy — and cost much less than the $1 billion that Bloomberg is reportedly ready to spend on a White House bid — to focus on shaping the next Congress.

A bipartisan gathering at the University of Oklahoma on Jan. 7, convened by former Sen. David Boren (D-Okla.), was designed to encourage a new centrist “government of national unity,” either by finding a major-party presidential candidate to champion it or by running an independent candidate. Bloomberg is a natural, given his moderate views, independent party affiliation and vast wealth.

Separately, a bipartisan group of consultants last year began promoting Unity08, a group that aims to hold an online convention to nominate either an independent candidate or a bipartisan fusion ticket.

As it happens, the surge by self-styled post-partisan Sen. Barack Obama (D-Ill.) reportedly threw a wrench into the Oklahoma City gathering, albeit a welcome one. This, combined with the New Hampshire primary victory by Sen. John McCain (R-Ariz.), who has been a maverick within his party, offers a sudden opportunity to refocus centrists’ efforts toward Congress rather than the presidency.

Focusing on the presidency is understandable. Installing a sympathetic president would offer the most powerful tool for instituting bipartisan governance; just consider how heavy a hand even a seriously weakened President Bush was able to wield from the Oval Office in 2007.

However, historically speaking, a third-party presidential victory faces exceedingly long odds. For more than two centuries, the Electoral College has proven to be quicksand for third parties. The system requires presidential hopefuls to score wins in a wide range of states in order to have any hope of winning the presidency.

The classic example is Ross Perot, who ran and lost in both 1992 and 1996. When he ran his first — and stronger — campaign, as an Independent, Perot secured an impressive 19 percent of the popular vote, yet he failed to win even a single electoral vote.

The reality is that third-party candidates win electoral votes only in unusual circumstances, such as 1968, when segregationist Alabama Gov. George Wallace won several Southern states worth 46 electoral votes as the nominee of the self- created American Independent Party. Even that haul was well short of the number necessary to influence the result, much less elect Wallace president.

Given the long odds of an independent presidential victory — not to mention the increased likelihood that a third-party candidate could siphon off enough votes to block a clear Electoral College majority, thus throwing the election into the House — the centrist movement might take a look at Congress instead. Shaping the House and Senate race by race is less sexy, and less of a boost to a candidate’s ego, than winning the presidency. But as a strategy, it might end up being more successful.

Imagine investing a modest share of Bloomberg’s theoretical $1 billion to establish an independent organization dedicated to centrism and bipartisanship. It could take the shape of a grass-roots membership group or a well-heeled donor organization or, more likely, a little of both.

The public face of the group would be a mix of respected Republicans and Democrats. Most important, the group would need to endorse both Democrats and Republicans running for the House or Senate, either as endangered incumbents or competitive challengers.

To get an endorsement, and the money or grass-roots support that goes with it, a candidate would have to demonstrate fealty to a bipartisan approach and centrist principles.

While many interest groups that endorse candidates today claim to support Members from both parties, the reality is that few of them regularly back Democrats and Republicans in roughly equal numbers. Most of these groups give solid support to one party but only token support to the other. By contrast, this new organization’s support genuinely would be up for grabs between Members in both parties.

If this group could endorse enough Congressional candidates, and if enough of them won, the group would find itself after Election Day with notable leverage in Congress. And given that the margins in both chambers of Congress are by historical standards quite narrow, the center is exactly where smartly applied outside leverage can accomplish the most.

Of course, the Republican and Democratic leadership in Congress would remain a powerful, perhaps the most powerful, force in determining how Members vote. But a well-funded, well-regarded outside interest group pushing for centrism and bipartisanship could become a third center of gravity, potentially upending the two-sided trench warfare that has driven recent Congresses.

Outside groups such as the Democratic Leadership Council and the Republican Main Street Partnership have worked in recent years to organize moderates in their respective parties. But while they share ideological common ground, they are at root partisan organizations, and as such aren’t well-placed to boost bipartisanship.

Meanwhile, caucuses such as the moderate-to-conservative House Democratic Blue Dogs are creatures of Congress. As such, their members risk becoming too dependent on party leaders. An outside force with money and people power might be able to throw around its weight in interesting ways.

Of course, a new centrist organization would put Members on the spot, forcing them to weigh their loyalty to the party against the ideals of bipartisanship and ideological moderation. Under the pressure, many may revert to the historical path of sticking with their party.

But particularly if an Obama or a McCain becomes president by promoting a bipartisan approach, this kind of organization could provide a ready-made caucus that could be leaned on to provide crucial leverage on hard-fought bills.

Moreover, many of those affiliated with the Oklahoma City group themselves served in Congress, including former Democratic Sens. Boren, Bob Graham (Fla.), Gary Hart (Colo.), Sam Nunn (Ga.) and Chuck Robb (Va.); former Republican Sens. William Cohen (Maine) and John Danforth (Mo.); plus current GOP Sen. Chuck Hagel (Neb.) and former GOP Rep. Jim Leach (Iowa). They should know how to push current Members’ buttons.

Because lots of factors played a role in heightening partisanship in American politics, from patterns of Congressional districting to the unfettered shoutfests of the partisan blogosphere, there’s no guarantee that a focus on the Congressional center would succeed in taking the edge off modern-day American partisanship. But it might be more effective than throwing money at a doomed presidential bid.

Louis Jacobson is the editor of CongressNow, which is published by Roll Call Group.