That would put Biden in a complete bind: he'd either have to acknowledge the US' capability to produce the oil we need and restore energy independence to the USA, or double-down on stupid and make things even worse.
It's a no-win for Biden and either way, this would simply increase consumer frustration with "why did this take so long?" (to restore our oil & gas industry here) or "WTF how is this guy so stupid?!" if he doubles down and starts calling it the Saudi Price Increase.
Yep, short-term horrible pain for long-term gain and a complete drubbing of the Democrat Party. Worth it, IMO.
Increasing US oil production to make the US energy independent is a fantasy.
First, even if the US increased production to equal demand, the price would be set by the international market, since any barrel that could be sold in Europe or Asia for more than is being bid by US refineries would be exported.
Second, embargoing exports is infeasible because the US oil is expensive to produce and depends heavily in the import of cheap drill pipe from Asia. That, in turn, depends on cheap iron ore from Australia and Brazil. If the US cut off oil exports, other nations would retaliate by cutting off exports of drill pipe, steel, and iron ore to the US.
The US has already mined most of its economic deposits of iron ore, and being independent in steel is even more challenging than being energy independent in oil.