I don't think anyone really thought it was possible to completely remove all blacks from the US, but it was one of a wide variety of solutions to the issue of racism of the period. For the most part, the people that went to Liberia were free blacks and largely paid their own way.

I'm not sure what the founders of the American Colonization Society were thinking on this. In 1820, the US census recorded that there were 1.5 million slaves in the country. That isn't counting the free black population (couldn't find a number, but I would guess half a million or a bit less). There was simply no way to move that many people (willing or not) across the ocean in a reasonable amount of time AND with the funds they could ever hope to raise.