Get it done quickly, and where it is most needed. Allow ranchers, groups of concerned citizens, States, and even Cities or Counties to finance their own needs, in their own timeframes, while ensuring high standards of interoperability and maintainability for DHS/ICE.
A $10 or $20 billion bill could be bitten off in $5 or $10 million dollar bites, from many sources. Organizations could freely arise to assist the effort.
Close the border! Surely you jest. The only ones that want a secure border are the American citizens. The politicians from both sides want it open, one for political reasons, the other for economic.
Then, 3 or 4 years ago, the AZ lege authorized the building of a fence with private money, but they finally shut that down for lack of money.