It's about to be flu season. They don't want hospitals to be overcrowded with paranoid patients because that means if somebody actually does have the virus they're less likely to get the proper attention. Etc. Not to mention all the people suffering from other problems. Such a strain on our healthcare system must be avoided at all costs.
This is a good thing, even if it is just a jumping off point.
The fact that this policy is intrusive, expensive and yet demonstrably irrational (at least on the part of the public) is pretty self-evident. The idea that we need some method, whether legal or social or both, to control irrational responses like this is a pretty a pretty natural conclusion after that.
Perhaps the idea that the government should not react due to irrational popular pressure is somehow libertarian, but really, it seems pretty non-ideological. Not wanting intrusions and restrictions on individuals just because a bunch of people are overly panicky is very reasonable.
Expensive: More expensive than not doing it, sure. There's only about ~150 people entering the U.S. daily from the Liberia+Sierra Leone+Guinea. The screens will be performed using digital thermometers. The cost should be relatively low.
Demonstrably Irrational: It's not really irrational to take the potential for public hysteria surrounding this issue very seriously. If people believe that we're just letting at-risk people travel freely between W. Africa and the United States then things are going to get very nasty the moment Patient 1 shows up (P0 died a few days ago). CDC (Frieden) admits that the checks might make people feel safer but the real focus needs to be on containment in Africa. Everything else is going to be a half measure by comparison.
To me, this is a great illustration of why we need strong, consistent rights and limitations on government action: it's not just a check on government abuse, or abuse by certain minority movements or even malicious abuse by the majority—it's also a check against popular emotional responses like this. It's a way of forcing ourselves to stop, reconsider and perhaps avoid acting poorly in a knee-jerk reaction.
(Also, thinking about it, it's a solid committment strategy: if these rights and restrictions are clear and unambiguous, we can use that when negotiating both with other countries and within our own government.)