Opinion writer

The presidential campaign is degenerating into gaffe vs. gaffe. On Friday, President Obama embarrassingly averred that the “private sector is doing fine” while arguing for his moribund jobs bill, which would spend billions to help state and local governments hire, in the unlikely event it passes.

Republican Mitt Romney replied that the president “says we need more firemen, more policemen, more teachers. Did he not get the message of Wisconsin? . . . It’s time for us to cut back on government and help the American people.” But that made Romney seem callous toward schools and first-responders.

Actually, though, this tiff has real implications for the debate, both here and in Europe, between advocates of fiscal austerity and of fiscal stimulus. Both sides should focus less on the amount of government aid and more on the degree to which it fosters structural reforms.

The president’s pitch for direct federal spending on public-sector employment is old-fashioned Keynesianism, adjusted slightly for the Democratic Party’s alliance with teachers unions. Education would get $30 billion of the $35 billion set aside for public-sector jobs in the Obama bill.

But the funding isn’t optimally designed, even if you accept the economic theory behind it. It doesn’t target states that are especially stressed financially. Rather, the money gets allocated according to state population. Even oil-rich North Dakota, which is running a billion-dollar surplus, would receive some.

If you look closely, nothing in the bill limits use of the money to teacher hiring and retention. Rather, it permits paying employees who provide “educational and related services.”

This is important. Although teacher layoffs are one significant way that school districts have dealt with budget cuts since the Great Recession, they are hardly the only way.

Custodians and front-office personnel have felt the ax, too, yet their role in training future productive citizens, another ostensible economic rationale of the bill, is rather tenuous.

Since the 2010-11 school year, more than 40 percent of education job cuts were due to attrition or declining enrollment, as opposed to outright staffing cutbacks, according to a survey of school systems by the American Association of School Administrators (AASA), published in March.

So when David Axelrod declares that “we have lost 250,000 teachers in the last . . . couple of years,” as he did on Sunday, he’s exaggerating. According to the Bureau of Labor Statistics, employment of all kinds in “local government — education” is down 224,100 since the recession began in December 2007.

Oh, and what measures were school systems least likely to use in order to avoid job cuts, according to the AASA survey? That would be reductions in health or pension benefits. Despite the potential for savings that could help preserve jobs, those perks are locked in by multi-year union contracts.

In other words, in the name of stimulating the economy, the president would shovel dollars into school systems regardless of specific need and without requiring reforms in return for the cash.

You could argue that the infusion, like previous rounds in the 2009 stimulus bill and in 2010, will enable schools to avoid drastic cuts — but it may also let them postpone structural changes that improve educational quality and long-term financial stability.

As for Romney, his remark implied a wish to “cut back on government” almost as indiscriminately as Obama wants to puff it up.

Wisconsin Gov. Scott Walker (R) on Sunday explained the real “message of Wisconsin.” “I know in my state our reforms allowed us to protect firefighters, police officers and teachers,” he said. “That’s not what I think of when I think of big government.”

Many school districts in Wisconsin have avoided personnel cuts because Walker’s reforms enabled them to trim costly benefits and work rules.

Walker added: “The ‘R’ after [Romney’s] name has to stand for ‘reformer,’ not just ‘Republican.’ ” But politicians of any party can be reformers, as the Democratic mayor of San Jose, Chuck Reed, has shown by supporting pension reform for that California city’s public sector.

The loose monetary policy and huge federal deficits of recent years helped prevent outright collapse — and bought us time to address long-standing inefficiencies in both the private and public sectors. We dare not blow this chance.

While getting its own house in order, Washington should use its leverage to generate structural change at all levels. Some say starve the government beast; others say feed it. The point, however, is to train it.