Republicans say the border is insecure, and they're right. Drug runners and other criminals do get through, and the problem needs to be vigorously addressed, just as terrorist threats must be dealt with.
The problem is, they conflate this issue of international crime with that of illegal, or undocumented, immigrants. These people are just looking for work, for a better life for themselves and their families than they can get in their native countries. They come to the USA because it is the land of the free, the land of opportunity. For the most part, they seek jobs which Americans are reluctant to take.
Immigration reform is related to, but different from, border security, and THIS is the issue that urgently needs to be addressed. True conservatives recognize this fact, though the false, loud "conservatives" of the right wing do not.