President Obama is expected to call for an extension of the payroll tax cut in his jobs speech tonight — in fact, it will likely be the centerpiece of his proposal. The tax cut, which was enacted in 2010 as part of the lame-duck tax deal, brings the employee share of Social Security taxes down from 6.2 percent to 4.2 percent. A few rumors are going around that Obama might even expand this cut further — perhaps by slashing the employer’s share of the tax. So will any of this actually help the economy?

The main point advocates emphasize is that an extension is necessary to preventing further economic harm. In 2011, the cut is projected to boost workers’ take-home pay by about $120 billion. If Congress lets the tax cut expire, then the hike next year would deliver an economic shock that could tip us back into recession. Goldman Sachs estimates that failing to extend the payroll tax cut could reduce economic growth by two-thirds of a percentage point in early 2012. Mark Zandi of Moody’s Analytics concurs. Even if renewing the payroll tax cut won’t boost the economy further, the argument goes, it will at least avert further degradation.

Indeed, a number of economists have recently tried to rein in enthusisam over the payroll tax cut. Former Reagan adviser Bruce Bartlett has argued that the measure doesn’t help the unemployed (who are most likely to spend any additional income), that it hits many higher-income Americans who don’t need the relief, and that many workers are more likely to pocket the savings than spend the money. It’s also not clear, Bartlett notes, whether the Social Security tax is even a tax — many economists consider it part of worker compensation. “In my view,” Bartlett argues, “the $110 billion cost of the one-year Social Security tax cut would have been far better spent on measures that would actively raise spending in the economy. Public works would be the best way of doing that.”

Now, there are two counterarguments here. One, even if workers are saving the money, that may not be so terrible. Plenty of economists have dubbed this downturn a “balance-sheet recession,” in which households are curbing their spending as they try to get their yawning debts under control. “If a payroll tax credit helps speed that deleveraging process along,” Stone says, “that’s not a bad thing.” And, of course, there are political constraints to consider. Additional infrastructure spending might pack more of a wallop than tax cuts. But Republicans are sounding somewhat receptive to a payroll tax cut extension; they’re not exactly giddy at the thought of massive new public-works projects.

Meanwhile, there are early indications that Obama might even propose expanding the payroll tax cut — say, with a holiday on the employer share. The logic is that this gives companies more incentives to hire by reducing the cost of workers. But plenty of economists are dubious about this proposal. Bartlett notes that only 4 percent of businesses cite labor costs as the reason they’re not hiring (most firms point to weak demand). It also makes a difference whether the tax cut goes toward firms that hire new workers or toward all firms — as Larry Mishel of the Economic Policy Institute points out, it seems bizarre to give free money to companies for workers they’ve already hired.

So that’s where we are with the payroll tax cut. The foundation of Obama’s jobs plan tonight is likely to be a measure that mainly just prevents further drag on the economy, doesn’t provide much additional stimulus, but is one of the few politically feasible ideas out there.