They are not a military threat (yet), but they threaten American interests in the region. Both Saudis and Iranians IMO are two sides of the same coin, and I agree with the fact Saudis are worse. US protects Saudi interests because Saudis sell their oil in dollars and Iranians dont. Most of their oil fields are on the eastern side of the Saudi Arabia, so a westward expansion of Iranian sphere of influence threatens that and the US dollar.
On top of it, China, which has just surpassed USA in oil imports, is pressuring Saudi Arabia to sell oil in yuan instead of dollars. If USA does not protect Saudi interests in the region, it will not hold its end of the petrodollar agreement and China will move in. That would be more disastrous than undoing the Iran deal.