Can the President have the military come and arrest you? Yes!
Can he (or she) send you to a military tribunal for trial or just hold you indefinitely in a military facility, without charges? Yes!
Even the bill co-sponsor, Senator McCain, appears to agree with this assessment. Senator Rand Paul asked John McCain, on the Senate floor, “…under the provisions, would it be possible that an American citizen could be declared an ‘enemy combatant’ and sent to Guantanamo Bay, and detained indefinitely?” McCain responded, “I think that as long as that individual, NO MATTER WHO THEY ARE, if they POSE A THREAT to the security of the United States of America, should not be allowed to continue the threat.”