I think that you are thinking of Texas Congressman Ron Paul. Officially, he is a Republican, but he casts his vote based on the Libertarian platform/philosophy. There are a few positions of them I agree with, but on this immigration issue they're lost.
The Libertarian philosophy on borders is totally out of lockstep with mine. The Constitution Party has the best platform on this issue that I have read. They basically have the same philosophy as Australia's One Nation party.
The Libertarian position, as I understand it, is that, with a dismantled welfare state, open borders would be a non-issue. Nobody would come with nanny state bennies in mind. Maybe somebody more familiar with the Libertarian position can clarify.
Of course, if you haven't dismantled the welfare state BEFORE opening the borders, you'll have a giant mess on your hands. Something like what we've got today.