An anonymous commenter offers some insight into the level of empirical research and logical insight that the famous institutions that campaign for Open Borders have brought to analyzing the long-run effects of their policy proposal.
In 1996 I had a brief conversation with David Asman, currently with Fox News, but then with the Wall Street Journal editorial page, and someone (as he noted in our conversation) involved with the "There shall be open borders" editorials.
I was one of the guests on a short lived and deeply stupid cable TV show Asman was hosting (Issues USA), and after the filming was done I took the opportunity to ask him about precisely your point: how many would come? He wasn't willing to spend much time talking about it (he was a busy man!), but what he did have to say was kind of..., um..., startling. He condescendingly informed me that people like me had nothing to worry about, because the number of people who would come to the U.S. under open immigration in fact wouldn't be many more than were already coming.
How did he know this? Well you see, the Journal had organized a trip down to a section of southwest border for some of its people. And when he was down there he saw with his own eyes that this stretch of border, despite being totally unprotected, was not being flooded by huge numbers of illegal Mexican immigrants rushing north, as the alarmists would have us believe. In fact he didn't see anybody! So why, he asked me -- given that nothing was stopping all of Mexico from coming here illegally right now if they wanted to -- did I think they'd suddenly all start coming if we made it legal?
I drove the road along the Arizona-Mexico border in 2003. Similarly, I didn't see a single illegal alien crossing it. Yet, for some reason, I didn't conclude that nobody was crossing. I surmised instead, from all the piles of junk left by crossers, by the holes bashed in the 4 foot tall fence every 100 yards or so, by all the testimony of locals I talked to, by all the news accounts I read in the local papers, that the illegal crossers were using the brilliant ploy of sneaking in at night because that's when it's dark! But then I'm not WSJ Editorial Board timber, so what do I know?