FORTUNE — Remember the sequester? The blunt, across-the-board cuts to government spending designed to deliver an austerity blast fell out of mind for most Americans back in April when Congress patched FAA funding to stave off an impending air travel nightmare. Planes kept taking off, more or less on time, and the broader predictions of economic cataclysm failed to materialize.

But the program is wreaking quiet havoc by boring into all sorts of other critical federal programs — clinical trials for cancer patients, Head Start help for low-income kids, in-home assistance for seniors, Western fire-prevention efforts, the post-Benghazi push to beef up embassy security, not to mention cuts to unemployment benefits, housing programs, public defenders, national parks, and on and on. The changes have been relatively small and diffuse enough to stay off the front pages, especially as the nation enjoys unexpectedly brisk economic growth.

That may be about to change. The first sequester cuts that could rattle the recovery are due to start hitting next week, as the Pentagon begins furloughing roughly 650,000 of its civilian employees across the country without pay for up to 11-day stretches, through September. Measuring any ripple effects from all those unpaid vacations could be tricky, since sequestration choked off funding for the Mass Layoff Statistics program, which the federal government uses to track and explain what happened whenever a company fires more than 50 people at a time.

MORE: Building the indestructible metropolis

But the bigger point is that it remains an exceedingly stupid approach to solving our deficit problem. In fact, it’s exactly backwards. As the International Monetary Fund noted earlier this month in its annual report to Congress on the United States economy:

“On the fiscal front, the deficit reduction in 2013 has been excessively rapid and ill-designed. In particular, the automatic spending cuts (“sequester”) not only exert a heavy toll on growth in the short term, but the indiscriminate reductions in education, science, and infrastructure spending could also reduce medium-term potential growth. These cuts should be replaced with a back-loaded mix of entitlement savings and new revenues, along the lines of the Administration’s budget proposal … A slower pace of deficit reduction would help the recovery at a time when monetary policy has limited room to support it further.”

In other words, a fragile recovery is the time to step on the gas, while signaling our intent to brake down the road. Then again, the whole point of the sequester was that it was bad idea: It was designed during the debt-ceiling standoff in the summer of 2011 to be so odious it would force both sides to the hash out a budget deal that would replace it with something sensible. That never happened, and it’s not about to, in part because the sense of urgency needed to dislodge anything from Congress is gone. “The big hit is dead ahead, when the furloughs start to kick in,” Moody’s Analytics chief economist Mark Zandi says, “but I’ll have to say that so far I’ve been surprised at how well the economy seems to be navigating through all the fiscal headwinds.” (Zandi figures fiscal policy is shaving off 1.5 points of GDP growth this year, with the sequester accounting for a third of it. If policymakers had cut that total drag in half, he says the recovery would now be evolving into a self-sustaining economic expansion.) From the right, AEI’s Kevin Hassett agrees at least on this point: Severe cuts now are the opposite of what this economy needs. “The smart thing to do would be to replace the sequester with medium and long-term cuts to entitlements that are significantly larger,” he says. And he even endorses some immediate new spending on job retraining to find the most efficient ways to get the long-term unemployed back to work.

MORE: This country needs another financial crisis

The next best chance to revive budget talks — and address the sequester — will come in the fall, when the federal government hits its borrowing limit, forcing Congress once again to raise the debt ceiling. Congressional Republicans are eyeing it as a chance to wrest concessions from the White House on tax and entitlement reform. Former Sen. Judd Gregg (R-N.H.), now head of the Securities Industry and Financial Markets Association and a co-chair of the CEO-driven Fix the Debt campaign, remains skeptical. “The work continues, not with great progress,” he says. “Without presidential leadership, it won’t happen, period.”