They, of course, would still work, but the great unwashed masses would sit on their backsides and take the money.
The counter argument would be the existence of industries that people will already not work in.For example Italy has a 38.5% youth unemployment rate. It also can't get enough workers for the garment industry. So why don't the youth of Italy want these jobs? Maybe the work is seen as menial (so a cultural condition) or maybe the wages are too low (they think they deserve more) or maybe Italy has made hiring citizens too difficult (so they shift to the black economy), but either way their reluctance is sustained by a welfare state that allows them to not work.
The same can be said in this country with the absurdly low unemployment rate in North Dakota while the disability rate has shot through the roof. Unless you think people have suddenly and inexplicably become disabled this is clear evidence that people are willing to go on the Government dole rather than get a job in North Dakota.
I'm not even saying these people are evil or irrational. (It actually seems entirely rational to me) In a similar situation I'd probably do the same thing.
The question is: how many people currently working would stop working if they didn't need to? (particularly in the areas vital for the basic functioning of society) That question is so impossibly difficult to answer that I don't think any system we come up with won't have potentially disastrous consequences.