I believe a politician with a decidedly anti-immigration platform, both legal and illegal, would get broad support. We have more immigrants in the country now than at any time in history, and the floodgates need to close for a while. Laws need to be enforced. Illegals need to be gone. Employers that hire illegals need to be punished.
Focus on this issue would put to rest the notion that the world hates America. If we are so hated, why are there more immigrants coming to America than to all other countries in the rest of the world combined?
Focus on the borders would help with national security issues. Not knowing who, what, and how many are coming across the borders is a recipe for disaster. Terrorism, public health concerns, document forgery, identity theft, fraud, costs to taxpayers, etc., are all related issues to not being able to control the borders.
I don't see a campaign against legal immigration winning any votes. I'd call it political suicide.