Absolute border security - it is literally impossible by land/sea/air/tunnel to cross into the US territory from Mexico without rapid detection and response.
...
Open border - the US does not impede general traffic from Mexico, bringing certain goods remains illegal but enforcement of this is limited to additional penalties after apprehension.
We are pretty far from both of those right now. I don't think the person you initially replied to was arguing for an open border. But surely it's not an ideal use of resources to stop all of these border based crimes in real time?
Most people are not crossing illegally. Those that do are going to have to actively evade those consequences as long as they continue an unpermitted stay. How much of our GDP should we spend to move "up" that spectrum? What benefits are we gaining by doing so? What consequences do we face?