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If Congress wrote specific border requirements into law, a future president would be legally obligated to operate within that statutory framework unless Congress later amended or repealed it or a court struck it down.
A future Congress could amend or repeal such a law, and future presidents would retain whatever discretion the eventual statute left to the executive branch. Courts could also determine whether particular provisions were constitutional or consistent with other federal laws.
The actual effect would therefore depend heavily on the language Congress adopted.