Sorry, but you absolutely CAN deport them faster than they can illegally enter--but not with current laws/regs. Which is why those laws and regs need to be vastly strengthened. EVERY law enforcement officer, local, state, and federal should be qualified to arrest any illegal immigrant he or she identifies, and such a requirement needs to be mandated for every city and state with a failure to comply resulting in all loss of federal funding for any and all programs. The action of a mayor telling his cops that they can't arrest illegals should get that mayor sent to jail on federal criminal charges.
It's not that the laws that are flawed, they are not enforced; since the laws in place are not being enforced, why would you think for a moment that new ones would be?
Explain how passing new laws would allow you to apprehend and deport 3 million illegals per year, while they are still streaming in, because there is no fence. Don't forget there are already millions here now to deport.