Aside from the offensiveness (to U.S. sensibilities, anyhow) of choosing May Day for the silly boycott/walkout, I don’t know that it’ll have a lot of effect on the economy.  There might be some spotty disruptions in some businesses if they rely heavily on illegals. 

As for the boycott, I just don’t see it having much effect.  At its core, it misfires by looking only at the numbers regarding the estimated purchasing power of illegals.  In order to have any effect whatsoever, it would pretty much require all the illegals to go home* (hmm…. maybe we can convince them it would be a form of protest ).  Consider the average household.  There are certain household expenses that you just can’t make go away.  Everyone has to eat (grocery expenses).  The ones who work have to get to and from work (transportation).  The kids need clothes, shoes, etc.  So even if the household makes a decision to purchase nothing on May 1st, it doesn’t change their overall consumption.  The effect of the boycott is simply to shift the spending to another day (heck, most people buy groceries at least weekly, rather than daily, so the only change that might happen is that they go to the store on Sunday or Tuesday instead of Monday). 

While some retailers might notice a slight hit in their daily numbers, the weekly sales are likely to be just the same as always, since the lack of sales on Monday will be offset on some other day.  This is the same reason why one-day boycotts of gas don’t work, either.  Unless you can convince the entire country to stay home for one day and not use any fuel, then the fuel purchase simply gets shifted from the day of the boycott to some other day.  The sellers end up with the same sales at the end of the week.

That said, should the work disruptions cause any sort of widespread problems, I would expect the whole thing to backfire on the organizers.  Instead of bringing the undecided over to their cause, the disruptions would only serve to foster a negative perception, which (even if not consciously) an undecided person will take with them from this point forward.

* It occurs to me that in some more insular communities that some people might choose to frequent only their local merchants on the idea that keeping it in “the community” will send a message.  The problem with this is that it’s not likely to be sustainable.  First, these local, small merchants typically have higher prices.  There is only so much economic sacrifice that the average family is going to put up with, especially if their income is low enough to be sensitive to small differences in price.  Eventually, these people will be back at Wal-Mart or whatever other big retailer has the best price.  Second, these small local merchants typically don’t have the selection of merchandise that people are seeking.  Once again, this will drive them back out to the Wal-Mart and back into the malls.