Well, it all depends...
(A) In the case in which demand for labor is inelastic--in which firms are going to hire more-or-less the same number of workers no matter what the wage is that they have to pay--then if you impose a FICA tax on employers it will be "paid" by the employers: employers will take a look at the old wage + FICA that they now have to pay, shrug their shoulders, and pay it. The wage that workers take home won't change as a result of the tax: but the total cost of hiring--wage + FICA--paid by employers will rise.
(B) In the case in which demand for labor is elastic--in which firms react to changes in the total cost of hiring by changing how many people they hire *a* *lot*--and in which supply of labor is inelastic--ya gotta eat, so ya gotta work--then the market will adjust to the imposition of a FICA tax on employers in a different way:
First, employers will take a look at the old wage + FICA that is now their cost of employment, say "it isn't worth employing the last 10,000 workers at this new cost of employment," and fire people.
Second, the fired workers will--through a variety of social mechanisms--push down the wage people get: with a long line of people outside ready to take the job at a lower wage, you aren't going to bargain too hard for wage increases (or against wage rollbacks).
The higher level of unemployment will continue to put downward pressure on wages until employers are once again willing to employ more people and thus push unemployment back to "normal". Where will that be? Well, it will be when new wage + FICA = old wage, when the total cost of hiring to employers is just equal to the old wage that they paid before the tax.
In this case, workers have "paid" the tax: the market's response to the imposition of the tax has generated shifts in wages and prices that have reduced worker wages by roughly the amount of the tax.
Most people I hang with think that (at least among the upper half of the working and the middle class) labor supply is relatively inelastic--that ya gotta eat, so ya gotta work--and that firms have immense freedom to alter their capital-labor ratios and staffing levels in response to changes in the relative price of labor vis-a-vis capital. Thus most people I hang with think that we are in case (B)--and that most if not all of FICA taxes levied on employers are actually "paid" by workers in the sense that changes in FICA show up as reductions in take-home pay, and not as reductions in firm profits.
But it's possible for things to be otherwise. Right now one of our assistant professors--Nada Eissa--is becoming the world expert on the Earned Income Tax Credit, a program that provides wage subsidies: if I remember my numbers, if you have two kids, the EITC will pay you an extra 40 cents on the dollar for the first $8,000 you make. The EITC is a program that is intended to boost the incomes of the worst-off strata of the working class. Does it work? Does it boost worker take-home pay, or is it mostly a subsidy to low-wage employers? The last time I talked to her she was saying that its effect boosting the take-home pay of the less-skilled was larger than its effect reducing the cost of hiring to those who employ the less-skilled. But the issue is far from settled...
Brad DeLong