(Simon & Schuster/HANDOUT)

The Senate’s filibuster agreement Tuesday gives the White House a chance to close in promptly — just nine months after the reelection — on filling some cabinet posts, specifically at Labor, the Environmental Protection Agency and perhaps the United Nations.

It’s most important to have Senate-confirmed appointees in these jobs, but the role of the president’s cabinet itself is much-diminished from Lincoln’s famous “Team of Rivals” weighing in on the Civil War.

“Think of the president as the head of Sears,” one astute observer noted, and the cabinet members as heads of the various divisions — Kmart, Lands’ End, Kenmore (“think of it as Treasury, it makes money”), the Kardashian Kollection and so on.

There’s not much need for them to meet with each other or the CEO — unless things are amiss.

As John F. Kennedy aide Ted Sorenson has written, Kennedy thought cabinet meetings were a waste of time. “No decisions of importance were made at Kennedy’s Cabinet meetings,” he recalled, “and few subjects of importance…were ever seriously discussed.”

In more recent times, according to data compiled by the incomparable Mark Knoller of CBS, Bill Clinton held 24 meetings in his eight years, including the Monica Lewinsky apology meeting after his testimony.

Occasionally, “you might call one because you haven’t had one in a long time,” a former Clinton aide said, but the gatherings were useful to have “coordinated messaging ”and team building, since members “rarely see each other” otherwise, he added.

A former George W. Bush White House aide noted there are “rarely significant substantive conversations on the issues” — those occur in “smaller subset groups” on foreign policy or the economy and such — and include senior White House staff.

But Cabinet meetings — Bush held 49, by Knoller’s count — are important, the aide said, to get across “the president’s perspective.” And then there are meetings “in the immediate aftermath of a crisis,” such as 9/11, which are critical to “convey a unity of purpose. . . and continuity of government.”

Obama has had some 21 cabinet meetings so far, running around 90 minutes or so. These also are held to coordinate messaging, to talk about the State of the Union Address, to review budgetary matters and so on.

But they also can focus on major events, such as the death of Osama bin Laden or the BP oil spill in the Gulf or efforts to boost the economy, a former Obama aide said.

Obama also can go off on other riffs — an analysis of the reelection results, or a reminder after the General Services Administration’s excessive conference spending for everyone to tighten up on such costs.

And before the budget is officially released, the cabinet members “have a chance to compare notes and to find out everyone” got short-changed, the former Bush aide joked, “not just them.”