I don't understand why this is going to affect "tens or hundreds of thousands of jobs"
The rigs are operated by employees of the international corps that run them, not the host countries they drill in or near. Unless I'm mistaken, the talent pool from which corporations hire is still largely here in the US, as are the best/cheapest refinement options, meaning most oil will end up back in the US eventually.
Ecuadorean wells, for example, were operated by Americans until their contracts ran out, and Alaskan rigs aren't operated by Russian employees who would be 10 times cheaper than the Americans who do run them.
Maybe you're making the argument that the market that provides services for rig employees may falter, but I have a hard time believing rig operators are going to up-root their families to the Middle East over a controversy that will be forgotten in a year, which means their families should keep the majority of the economies they influence unaffected.