Mitt Romney is fulminating again about President Obama as a practitioner of an odious “Chicago style of politics,” redolent with its implicit suggestions of dark alleys, shadowy tough guys, the passing of money-filled envelopes and rhetorical, maybe even physical, violence.

He and his supporters are peddling a woefully anachronistic caricature. They know not of what they speak.

It was thus no accident that when a principal and parents sought counsel Tuesday from a Chicago alderman about finding money for their hard-pressed elementary school, his advice was concise: organize to gin up neighborhood support, raise the school’s profile and ultimately impress the public schools hierarchy.

Alderman Ameya Pawar, a young and earnest former university emergency-management specialist and the son of Indian immigrants, didn’t ask for cash to put in a fix or signal whom the small group should intimidate. Sitting in his North Side office, he proffered old-fashioned, even quaint, ideas to gain influence.

Huh? This was Chicago politics, and from a Barack Obama partisan, no less? It seemed more like politics in Buffalo, Omaha, Houston or even some leafy suburb. Romney would apparently be shocked.

Romney moaned Monday about the Obama campaign deriding his Bain Capital years and said, "They're misdirected and I think the American people recognize that kind of polities is something of the past. It may work in Chicago, but it's not going to work across America."

Ed Gillespie, a top Romney strategist, picked up the frequent GOP refrain, about those awful "Chicago-style politics" now enveloping ever-saintly Washington, D.C. , while talking to reporters.

For sure, Chicago was once home of the Democratic "Machine" whose most nimble practitioner was the late Richard J. Daley, "The Boss" and most potent big-city executive of his era. His universe was one of bloodless pragmatism, big plans and effectively servicing most constituents, and was certainly filled with ample nepotism and bad actors.

But for many reasons, the Machine is largely gone, in part due to several decades of court orders demolishing the patronage system and ward structures that were its lifeblood. At the same time, the image of blue-collar Chicago has been upended by its evolution into one of the most cosmopolitan world metropolises with booming white-collar service and other industries.

Economically, its international clout is often ranked just behind that of New York, London, Singapore, Tokyo and Paris. Its theater is world-class; the dining sector is a breeding ground for superstar chefs; and its universities are among the best and most intellectually influential. It’s why rising Chinese legal academics are to be found this week at a University of Chicago conference.

Even with shameful poverty and crime, it's also a beautiful town. The downtown Millennium Park constitutes one of the most stunning new public spaces to be found anywhere.

Its politics are far more complicated than Romney or Gillespie apparently understand, though they should know better. There are many circles of influence and many adroit, if at times feuding, practitioners. There is no one “Chicago style.”

Obama is a Harvard Law School graduate and former South Side community organizer who succeeded despite the lingering influence of the dying machine, by then led by Daley's son, Richard M. Daley, who served as mayor for 22 years before stepping aside last year. He didn't seek nor get much help from the machine and kept his distance. Many Daley loyalists harbored deep suspicions about a fellow they deemed effete and aloof.

So Romney and Gillespie can essentially lump Obama with the likes or Republican George Ryan and Democrat Rod Blagojevich, the former Illinois governors who are now both in federal prisons, and the many Chicago aldermen who have been convicted of crimes.

And they can hammer away at Chicago as a political den of iniquity, while apparently being ignorant of Justice Department surveys on municipal corruption that always show Illinois ranking well below the leaders of the pack, such as Florida.

And they're apparently ignorant of the past or current dealings of Obama aides and alumnae, notably Chicago Mayor Rahm Emanuel, re-election strategist David Axelrod and recent White House Chief of Staff William Daley.

These are not the Super Fans of "Saturday Night Live" lore, made famous by the likes of George Wendt and the late Chris Farley: beer-guzzling, bratwurst-chomping Chicago partisans heralding "Da Bears!"

All have been sophisticated political practitioners on the national stage for more than two decades. They’ve called Chicago home but transacted business all around the land for many corporate and political clients. Republicans should be impressed by how very well each has done in the private sector.

Bill Daley was Commerce Secretary and helped run a major telecommunications firm. Emanuel, as a then-upstart congressman, slapped the Democratic Congressional Campaign Committee into shape as its leader when the party retook the House of Representatives in 2006. Axelrod has plied his tactical aplomb nationwide and will go down in history as having discerned earlier than almost anyone the possibility that a little-known black politician could become president.

They’ve traveled the world and are as at home seeking contributions in the Hamptons or Beverly Hills as they might be having a Bud at U.S. Cellular Field as they watch the White Sox. Their collective Rolodex would be prodigious.

But to hear Republicans tell it, the three are products of a nefarious culture that serves as a real-world extension of Mario Puzo's fictional Corleone family. It's why GOP critics should watch the scene in "The Godfather" where hulking Luca Brasi, Vito Corleone's enforcer, seeks to infiltrate the opposing Tattaglia family but winds up sleeping with the fishes, murdered by a Tattaglia boss who smelled a rat.

Well, if Axelrod, Emanuel or Daley ever came Romney's way, the Republican camp would be smart to lure them into the fold, rather than blindfold and tie them perilously to a jet ski on a desolate New Hampshire lake.

Either may be far sharper than most of the folks in the Romney camp; you know, the ones making Republican partisans like Rupert Murdoch and William Kristol anxious about the mere competence of the Romney campaign.

Indeed, if Republicans looked at Emanuel's 14 months as mayor, they might want to steal from his policy playbook. He's taking on unions, forcing efficiencies in government, dramatically lengthening the school day and spurring private-public infrastructure partnerships.

A lot of traditional liberals are feeling a bit queasy but, given the city's awful economics he inherited, he is doing what he's got to do, often irrespective of ideology.

Being shrewd, tactical and conscious of bottom lines. Getting stuff done. That’s often the Chicago way of politics and, more often than not, worthy of emulation, not ignorant derision.