Crossing the Mexican border illegally gives you the highest chance of getting caught. One can safely assume that real terrorists will seek to minimize their chances of getting caught during infiltration.
Landing by whaleboat on a deserted beach is much easier. Crossing from Canada is much easier. (And the Canucks will let you mooch off their welfare system for quite a few years--all you have to do is say "I'm (name not in Canadian terrorist database) and I'm a refugee." Hell, they'll put you on the fast track to Canadian citizenship.)
BTW, the last method makes you legal, and allows you unlimited access to the United States. It's not even a matter of overstaying a tourist visa. It is the safest means of infiltrating the US.
If you want to shut off illegal immigration from Mexico, say so honestly, and be prepared to justify the costs based solely on the benefits of shutting off illegal immigration from Mexico. It will not stop one single terrorist from entering this country. Selling it as an "anti-terrorism" measure will last until thwe terrorists outsmart you...and then you will have one hell of a credibility problem.
Such a statement must logically presume that not one single terorist infiltrate from Mexico...which is not a credable statment.
As to it giving you the highest chance of getting caught...I can't say statistically, but I do not believe that such a statement is supported by the stats. Even if it were...the statistical chance is what is important given the numbers coming across.
I grant that coming ashore and coming through Canada are vulberabilities as well. We need to do the best we can do on all fronts and we can do more in each area. That's all. We are all on the same side here.