For the Washington fantasists who like speculating about what might have happened in policy and politics “if only,” one of the most interesting questions at the moment is this: How would the administration be faring now if only Tom Daschle had properly paid his taxes.

Part of the answer, especially in the past week, has become this: Maybe not all that differently, because so many veterans of his old Senate staff are now packing into the West Wing.

It was five years ago Wednesday that President-elect Barack Obama announced the former majority leader would be returning to government as Health and Human Services secretary, where he would be in charge of drafting legislation overhauling the health care system and then steering it to enactment.

The choice seemed an obvious, but astute, way to boost the likelihood that the new president’s top domestic priority would move through Congress relatively smoothly and quickly, and to assure the bureaucracy would then implement the inevitably complicated changes to medical insurance rules with minimal fuss.

But less than eight weeks later, Daschle withdrew his nomination after concluding that getting confirmed by his former colleagues would be an uphill battle — one requiring Obama to spend too much of his initial stash of political capital. The unsolvable problem was that after becoming the first Senate leader in half a century defeated for re-election, the South Dakotan stayed inside the Beltway and took on a range of lucrative consulting gigs — but did not retain a good tax accountant.

He volunteered to Senate investigators that his returns from 2005 through 2007 had serious mistakes (the biggest was not reporting as income the car and driver he had as part of a business deal), and he paid $140,000 in back taxes and interest. But those moves could not swiftly save him at a time when Obama was promising to change the ethical climate in the capital and to distance his White House from the revolving doors along K Street.

It was a humbling end to the public career of someone elected Democratic leader after less than eight years as a senator, as well as someone who had only recently loomed as a top-flight presidential prospect.

Daschle, who turned 66 on Monday, now embodies the archetype of the Washington elder statesman — out of the limelight, but hardly out of influence. He’s a top rainmaker at the premier lobby law firm DLA Piper, where he’s got sway in the financial services, telecommunications, trade and tax worlds in addition to health care. He’s also on a range of public and private boards. And as a founder of the Bipartisan Policy Center, he is regularly called on to explain the current congressional calcification and to prescribe ways for ending it.

His most extensive and enduring influence, however, looks to come through the people he employed during his quarter-century in Congress. He’d been a Hill staffer before his House election, and soon thereafter started cultivating what’s become a legendary staff alumni association. (The network’s influence on public life may only be exceeded by the legions who once worked in the Senate for the late Edward M. Kennedy.)

Daschle’s sway was helped significantly by his decision to get in on the ground floor with his investment in Obama’s future. After the obscure state senator won the Illinois Senate primary in 2004, the caucus leader made himself available to help with the rising star’s near-certain transition to the Senate.

When Daschle lost that fall, he steered several of his top staffers Obama’s way. Among those who soon helped engineer Obama’s improbably rapid trip to the Oval Office were media expert Anita Dunn and deputy campaign manager Steve Hildebrand.

Three more veteran Daschle staffers were not only the 2008 campaign brain trust, they headed straight away to the West Wing — where, as of next week, they will all be reunited for a while.

Denis McDonough was Daschle’s senior foreign policy adviser, did that job for Obama/Biden in 2008, started as National Security Council staff director the next year and rose steadily to take the corner office as White House chief of staff a year ago.

Phil Schiliro took a year, in the middle of a two-decade senior House staff career, to serve as Daschle’s final policy director. He ran congressional relations for the Obama campaign and was top White House lobbyist for the next two years, the most legislatively successful of Obama’s presidency. And now, for the next several months, he’s setting aside his new life in New Mexico consulting for nonprofits in order to take some pressure off McDonough, who has been shouldering most of the work shielding the health care law from Republican efforts at repeal and Democratic congressional criticism about its troubled implementation.

And Pete Rouse, who spent almost two decades among Daschle’s top aides, was Obama’s first Senate chief of staff and has been his trusted confidant and fixer ever since. He did a short stint as acting chief of staff three years ago, but has preferred to stay away from the public eye. And now he’s said to be planning to leave the administration within the month.

It’s that vacancy that has created an opening for a West Wing curtain call by one of the most prominent Daschle alumni of all: John Podesta, who spent 1995 and 1996 as the hand-picked top counsel to the newly installed Senate minority leader. (He left for the White House, where he was chief of staff for the final 27 months of Bill Clinton’s presidency, starting with impeachment.)

Word spread Tuesday that Podesta, a regular but informal adviser since running Obama’s 2008 transition, will soon go back on the government payroll as senior presidential adviser and will stay for the next year. That means he’ll help shape a very lean 2014 legislative agenda, then help the president leverage his executive authority as a way to notch some accomplishments before the midterm elections.

For a while after the health care rollout meltdown, there was buzz about Obama calling on his old mentor Daschle to help reverse the situation. The newly configured crisis management team means the president has decided on a classic Washington alternative: The staff can handle it.