Nice guy though he is, Sen. Ben Nelson is like the Platte River in his home state of Nebraska: broad and slow-moving. He is an insurance lawyer by trade—small-town, soft-spoken. But in the Senate last week he was getting the Susan Boyle treatment, surrounded by reporters eager to hear his every word. I was one of them, because Nelson—and a handful of other Democrats who call themselves centrists—are suddenly key to the new arithmetic of power in Washington, D.C.

Since Election Day, Democrats have dreamed of reaching the sunny uplands of a filibuster-proof Senate majority. Now that Sen. Arlen Specter has switched parties, and Al Franken seems likely to win his vote-count court case, they are approaching the commanding heights. But they ought to be careful what they wish for. The history of fat congressional majorities is mixed. They can stoke unrealistic expectations among interest groups and magnify the role of outliers and egos. There is a risk of philosophical overkill, internal civil war and the kind of political myopia that eventually empowers the opposition party (yes, even one as lost as this GOP).

The country's philosophical fault lines don't disappear when one party is in power; they just appear as internecine battles. If and when the Democrats get to 60, the party's core liberal-progressive interests are likely to demand prompt action on a host of topics. But if every action requires 60—and that's becoming the norm in the Senate—the ironic result will be to empower the party's centrist wing. "We're going to spend all of our time dealing with those guys, I'm afraid," said a Senate leadership aide, who declined to be identified because he didn't want to antagonize them.

Take Nelson. He voted against President Obama's budget; doesn't want to give bankruptcy judges power to "cram down" home-mortgage payments; is wary of taking on credit-card companies that charge high interest rates; and is skeptical of "card check," labor's top legislative priority. He also opposes a "public option" on health care—"That would be a deal breaker for me," he says. (Eighteen other Democratic senators are on record saying that any reform without such an option is a deal breaker for them.) "I'd remind the president that having 60 members does not equate to 60 votes," Nelson told me.

Specter won't be any more tractable. Just dealing with him could be a full-time job, as it was for top Republicans. Obama and Sen. Harry Reid promised to support Specter's candidacy for reelection next year as a Democrat. Their operating assumption was that Specter would help pass health care, which may be true, and that his status as a new Democrat facing a primary would pull him to the left. But his first votes—on the budget and mortgage rewrites—were against the administration.

Specter poses housekeeping problems as well, which seem trivial but loom large in the status-obsessed Senate. Reid promised to honor Specter's seniority while not "bumping" any committee or subcommittee chairs. How Reid does this without offending the prickly Specter or the existing chairs is unclear. "We don't play bumper cars here," said Sen. Barbara Mikulski. (Translation: get in line, bud.)