This is why atheists shouldn't reference the Bible, because they aren't Biblically educated enough to make sense of it. You're applying the bible to modern times when it was written years ago under different principles. You literally took scriptures from the book of Romans, an era which the government was Christianity and Christianity was the government. There was no separation of church and state, therefore, the meaning of "Everyone must submit to governing authorities. For all authority comes from God, and those in positions of authority have been placed there by God..." holds true because, then, the government was indeed established by god. The laws were the Ten Commandments.
In America, the laws are established by men, therefore, Bad Onion is correct by stating "We must obey god as ruler rather than men".
There may seem like there is a contradiction at the surface, but a good Christian who reads their Bible everyday...