The US drillers have stopped drilling, but it obviously makes no sense not to produce if the wells are already drilled. The US wells in production will deplete much faster than the wells in Saudi Arabia, probably falling 30% by the end of the year. The Saudis will also be unable to keep up production without stopping for maintenance, so prices are quite likely to tighten a little in the near-term. They might not go high enough to justify new drilling in the US, so the Saudis might just get their wish - stable $70 oil.
Not all of them