Limiting imports, even banning them would shoot the price of oil up again but as the frack wells come back on line and people drive less because of the higher cost the price will drop and drop some more.
Actually, if we stop importing oil, the world oil price would collapse. There would be 4b barrels a year more oil on the world market which would be a huge glut.
Of course, oil prices here in the US would skyrocket. The article says it would exempt Canada and Mexico, so what would actually happen is that they would sell ALL their oil to us and nothing to anyone else in the world. So prices would not skyrocket but would rise to whatever the local shortage would be while US, Canadian, and Mexican producers ramped up. Other countries would still face a glut and enjoy lower oil prices than us. We might even find Mexican companies buying oil on the world market and selling it on to us claiming it was produced in Mexico.
Overall, not a very clean solution. Price guarantees would be cleaner without costing a dime. US producers would be assured OPEC couldn’t pull the rug out from under them, and opening up more federal lands including ANWAR would lower production costs. Not free market, but then again OPEC is not a free market player.