Joseph
This is another impossible dream. The Government even under Obama has been deporting illegal aliens. The problems are:
A) Unless they are in jail even if they (illegal aliens)are caught they are usually let go and told to come back for their hearing, which most of them never show up for. The only way to show you really mean it is to keep them jailed until the hearing.
B) There is no real solid wall or fence dividing the US from Mexico or Canada so you can just walk across or swim in some places. A solid wall with trip wires are needed to prevent the illegals from entering the US. So even if you deport a few they just keep coming back. They have been talking about building a fence for years but nothing has been done.
Likewise, better control over people who remain after their visa expired is needed so that they can be rounded up and deported.
You are going to need a new police force and prisons just to handle this. But can we afford this?