This provides the background data for a post I plan to write tomorrow. That post will be my fantasy policy making post on what immigration platform I'd have if I had a massive stroke that caused sufficient brain damage to make me want to run for Congress and suffer through all that nonsense. It's what I think we'd have to do to have a working border policy, not anything that I see coming up for debate any time soon.
Some very limited discussion. First, as you can see there is likely some deterrent effect. It's also mostly swamped by the economic effects. I'd add that based on some historical points I've heard made that a massive increase in draconian enforcement would likely lead to a sharp drop in border crossings. I'd also say based on historical data this drop would be temporary since those crossing can adapt faster than government can respond to adaptations. The cost figures I have are for border patrol only, there is also substantial expenditure on inland enforcement, such as workplace raids. From these reports it seems that interior enforcement is much more expensive than point enforcement at the border. There is no hard data given on this so you can choose whether or not to believe this. I do think it's unavoidable to conclude that an enforcement first approach is futile, the additional resources are having an impact but it isn't that large and is likely to suffer from diminishing marginal returns.
Feel free to dig into the data yourself.
People Crossing Borders: An Analysis of U.S. Border Protection Policies
Border Security: The Role of the U.S. Border Patrol
Remember, these are reports for Congress. Whatever it is they're saying they do know this stuff, or at least have a staffer who does.
[In case it wasn't clear, all data from the above two linked reports]