In politics, having a good memory can always be something of a liability. It was, after all, only a couple of decades ago that Bill Clinton was one of the leaders of the centrist faction of the Democratic Party and his presidency is considered to have succeeded in large measure because of his decision to distance himself from liberal dogma. Nevertheless, both the former president and his spouse—who hopes to return to the White House in 2016—were front and center at the inauguration of Bill de Blasio as New York City’s new mayor. The event was a celebration not just of the new mayor but of the leftist ideology he championed during his campaign. Class warfare was the theme of the day articulated by a blistering diatribe by new Public Advocate Leticia James, in a poem recited by a college student, and repeated by de Blasio when he said the chief purpose of his administration of the country’s largest city would be, as the New York Times noted, to “fix” inequality in Gotham.

This theme may dovetail nicely with President Obama’s attempt to change the focus of the national political discussion from one about the impact of his disastrous health-care law to one about populist initiatives such as an increase in the minimum wage. But it also represents the kind of muscle flexing on the part of the party’s liberal base that hasn’t been seen since Clinton’s so-called “New Democrats” took control of things in the early ’90s. And that is exactly why Hillary Clinton and her ubiquitous husband were eager to associate themselves with not only de Blasio’s victory but also with the leftist surge that brought him to office. Having failed to win the presidency in 2008 because of an inability to defend her left flank, Clinton seems determined not to make that same mistake in her next try for the White House. But the question remains whether worrying so much about liberal sensibilities is the smartest thing for her to do in the long run.

It is true that the alliance between de Blasio and the Clintons runs both ways. The mayor ran Hillary’s first Senate campaign, but his political roots are to be found on the party’s far left and he was never part of her inner circle. By having the former president rather than a judge or some other public figure swear him in, it could be said that de Blasio was attempting to associate himself with the Clintons’ pragmatism rather than the other way around. Indeed, as the Times noted in another article on the inauguration, de Blasio is hoping to use the Clintons to keep the city’s business interests from open opposition to his administration, something that is a potential problem for the mayor given the tone of the anti-capitalist rants he and his followers have been sounding.

Yet both Bill and Hillary are past masters of the art of putting their fingers to the wind to determine their future course of action. And since the wind in the Democratic Party is blowing hard to the left these days, their decision to make de Blasio’s inauguration an official Clinton affair must be understood as an indication of how Hillary perceives her current political dilemma.

Clinton lost the 2008 Democratic presidential nomination largely because she was seen as the centrist in the race. That resulted in her left flank being left wide open for Barack Obama to ride a wave of anti-war sentiment to the White House. Having seen how poorly such a stance played to Democratic primary voters, Clinton is obviously determined never to make the same mistake again. And given the resurgence of the left wing of her party, a tilt in their direction would make it harder for potential gadfly candidacies from people like California Governor Jerry Brown or former Montana Governor Brian Schweitzer to gain traction in the winter and spring of 2016 or a more mainstream challenge from Vice President Biden. As we have seen throughout the past months, this time the Clintons are leaving nothing to chance when it comes to the next presidential election–and if that means spending as much if not more of their time echoing the left’s rhetorical excesses about inequality as kissing up to their usual Wall Street donors, so be it.

But Clinton needs to be careful about identifying too much with the de Blasio faction and other left-wingers. Though they are the flavor of the month today as the White House tries to sound similar themes, hitching her star to the mayor’s wagon may not seem like such a brilliant idea if his “progressive” administration really does go to war against business as well as reversing police procedures that have kept crime rates down in the Big Apple. If tax increases start to chase business and the middle and upper classes out of the city, Clinton may find by 2016 that the association with the mayor is as much of a burden on her hopes to win the presidency as it is an asset.

More to the point, a shift this far to the left is going to necessitate a swing back to the center if, after easily winning her party’s nomination, she wants to win in November. The problem with Clinton in 2008 wasn’t as much her centrism as it was her lack of authenticity and inability to connect with voters as well as Obama. Politically motivated ideological mood swings will only remind voters of their previous doubts about her. Just as important, anything that distracts the public from her sales pitch to be the first woman in the White House is a mistake.

The Clintons’ embrace of de Blasio is a tactical stroke that makes a lot of sense right now. But over the long haul, it may be yet another example of Hillary’s predilection for being too clever by half.