We aren't shipping refugees here to do labor. There's no work for them to do. That shouldn't even be a consideration in today's context. And since the government can just print whatever money it needs the cost is no object.
Something to understand:
In the existing state of political economy we pay taxes so people will have use to federal currency, not to fund the government so thinking like professor's is out of date. The taxpayer doesn't actually "pay" for anything. The reason it's set up like this is to lock people into the established system, not to fund things the government would like to do.