Yes, the cost would be a large chunk of our GDP; why is that a problem? Where else should that much of our GDP go, if not to food and shelter for people?
And how much would our GDP improve if, all of a sudden, we had a strong consumer base, again? I'm not an economist, so I can't run the numbers, but it seems obvious that the economy as a whole would improve massively.
We've been hearing the rhetoric that tax cuts increase tax revenue by stimulating the economy for decades, and that's true, IF, and only if, the tax cuts go to people who will spend more money. The problem is that they keep giving the tax cuts to rich people, who don't spend it, which leads to lower revenue and an even worse economy.
A Universal Basic Income is just the reverse; give money to people who sill spend it on goods and services, and it will drive the economy.
In an era where increased productivity and technology has radically improved the ability of an individual to accomplish work, it is only natural that fewer and fewer jobs will become available, and there is a strong argument that many jobs that exist today are make-work programs; effectively a UBI for certain people. We need to extend it to everyone, or there are going to be a major problem.