Even setting aside the politics of privatizing the VA, as the Speaker vote demonstrated yesterday, the margins for the GOP are *tight*.... zero room for error.
I'm sure the strategy will be to carry a massive bill with every single Trump priority through reconciliation, and I'm sure he'll use all his political capital to get it across, but as a standalone item, a privatization of the VA wouldn't stand a chance in the House (and would probably have significant issues in the Senate tbh).
The same probably holds for most of the things that "DOGE" wishes to cut. When you have a 220-215 majority in the House, just on math, you don't have a "mandate"