Greg Mankiw and Bryan Caplan make the same point about Obama's payroll tax: it might better have been done on the employer side.  Bryan makes the argument much more forcefully, so I'll quote from him:

With perfectly flexible wages, it doesn't matter whether tax law says "employees pay" or "employers pay."  Tax incidence depends on supply and demand elasticity, not legislative intent. If wages are nominally rigid, however, the law matters.  If you cut a tax on employers, this reduces labor costs, increases the quantity of labor demanded, and reduces surplus labor.  If you cut a tax on employees, in contrast, this increases worker compensation, increases the quantity of labor supplied, and increases surplus labor.

In both cases, admittedly, a tax cut might directly increase demand and, with nominal wage rigidity, increase employment.  But when you cut taxes on employers, the incentive effect and the fiscal effect work in the same direction.  When you cut taxes on employees, the incentive effect and the fiscal effect work in opposite directions.

That's why Obama's proposed payroll tax holiday botches anidea of truly Singaporean cleverness.  Instead of giving the tax cut to employers, where it would do the maximum good, or splitting it evenly, where it would do intermediate good, he's giving all of it to employees, where it does the minimum good
Given the terrible jobs figures, it seems obviously more important to me to pick the tax that is most likely to stimulate employment.  Employed workers are mostly doing fine in this recession; it is the unemployed who need help, desperately. 

But I see the payroll tax as a fundamentally political move, not a serious attempt to fix the economy.  Cutting payroll taxes on workers means they will notice a little more money in their paycheck, and be happy with Obama.  The unemployed won't be any happier, of course, but they have extended benefits, and few of them will realize that a differently structured tax cut might have given them a slightly better shot at finding a job.