WASHINGTON — The vice president calls, more than an hour after the appointed time but with an impeccable excuse: He was presiding over the Senate’s vote to ratify the New START treaty.

START was the finish of a great few weeks for Joe Biden. A great few weeks for President Obama, too, but in a sense even better for Biden because so many of the successful initiatives were on the vice presidential to-do list.

Deal with the expiring tax cuts? Check, after hours of negotiations around the vice president’s dining room table. Pass START? Check, after dozens of vice presidential interventions with wavering senators. New government in Iraq? Check, in the wake of a presidential assignment, “Joe, you do Iraq.”

It is easy — literally, folks — to mock Biden, but it is even easier to underestimate him. He is reliable fodder for late-night comedians. He is like an overeager puppy with a tendency to rhetorical accidents that require cleaning up. The latest was his assertion, about Afghanistan, that “we’re going to be totally out of there, come hell or high water, by 2014.” Totally, that is, in terms of combat troops. When Biden talks, folks, you can’t necessarily take him literally.

But Biden has also turned out to be a particularly effective player for the Obama administration across a broad spectrum of issues — and one whose political skills and relationships on Capitol Hill may turn out to be even more important in the new, post-election reality.

Biden is the happy creature of an institution that Obama couldn’t wait to escape. Those relationships — the proven value, as he likes to say, of “my word as a Biden” — along with his well-honed sense of how far any individual lawmaker can be pushed, will be tested early in the 112th Congress.

The notion that this is a new function for Biden, filling a vacuum left by the departure of Rahm Emanuel, is wrong. As the vice president will be the first to tell you, even if you haven’t exactly asked it that way.

How has his role evolved, I wonder? “The story line emerging — Rahm’s gone, Joe jumps in — I have been doing this stuff from the beginning,” he says. “I’ve been dealing with Republicans from Day One, and I’ve showed up at every critical juncture when we needed the House. Last year the guy Nancy (Pelosi) wanted to come and speak to their retreat was me.”

The fascinating thing about Biden’s evident insecurity — “Here’s the thing I tell people and I realize I’m too colloquial and they think I never read anything and I read more than most of them,” Biden says at one point, apropos of nothing — is that, at least as far as his role in the administration is concerned, it seems unwarranted. For example, with little fanfare, it was Biden who helped broker the last increase in the debt ceiling in January, part of a multiple-moving-parts deal that also created the deficit commission.

Can that trick be repeated, once the warm feelings of the lame-duck have yielded to the cold reality of a Republican House and shrunken Democratic majority in the Senate? The answer will come early in the new year, with the debt ceiling about to be hit and funding for the federal government set to expire March 4. The linkage could give Republicans a powerful club to insist on punishing cuts.

Biden, chronically optimistic, might be forgiven a burst of Christmas cheer. “The one message (of the election) was, we want you guys to cooperate where you can,” Biden says. And, he insists, Senate Minority Leader Mitch McConnell was among those who “got the message.”

Really? Mr. “If they think it’s bad now, wait till next year”? Mr. “The single most important thing we want to achieve is for President Obama to be a one-term president”?

Look past the political rhetoric, Biden advises. “Don’t be moved by all you hear and take a look at what their needs are. … We don’t have a whip hand but it’s not so clear they have one,” he adds, noting that a Republican push for immediate and drastic spending cuts will run headlong into economists’ warnings about the impact on a still-fragile economy.

“There’s going to be a lot of room here. It is not set, match, in my view.” With that, Biden is off. The vice president of the United States has, literally, a train to catch. The 4 o’clock Acela, home to Wilmington.