One of the problems regardless of who patrols our borders is that we have so many of them. A very large percentage of our borders are water accessible. When you throw in the water accessible part of our Navigable waterways you can see that it is nearly impossible to secure them. To adequately patrol our borders (forget for a second who it is, military, Border Patrol, INS, Coast Guard, Local Police...) will require not 25-35,000 additional bodies but hundreads of thousands of bodies. Even if we did decide to devote the resources needed for that task, there are still the inland airports and hidden access (bodies in containers, people overstaying visas, no way to track continental movement) issues that need to be addressed.
The fact is, until we are willing to accept some method of identifying who IS a citizen, it will be nearly immpossible to detect illegal aliens.