Can the boarder patrol stop you if you arent crossing the boarder.?

So some friends and I are traveling to South Padre TX for spring break this year. Someone said that the Boarder Patrol have a checkpoint set up leaving padre where they stop you and could search your car. If you are american citizens and haven't left the country or crossing the boarder can they stop you and... show more So some friends and I are traveling to South Padre TX for spring break this year. Someone said that the Boarder Patrol have a checkpoint set up leaving padre where they stop you and could search your car. If you are american citizens and haven't left the country or crossing the boarder can they stop you and demand to search your vehicle?

(We arent planning on doing any illegal and it wouldnt matter if they did search us because of that, I am just curious of their rights because that sounds like a load of crap to me).
Update: To clarify, we will never be leaving the United States, we will be in South Padre TEXAS. The check point is said to be on US soil leaving South Padre TEXAS
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