This of course depends on what tyranny means. The general definition is 'the arbitrary or unrestrained exercise of power'. To me the key term is 'unrestrained'. In the United States we theoretically have three co-equal branches of government that are supposed to check each other. But those checks appear to have failed. As evidence just take a look at an article published in the Washington Post. What we see there is a well enumerated list of powers that are now held by the Presidency. Powers that explicitly allow for the unrestrained use of power by the President. As explained in the article any President of the U.S. can:
Order the killing of anyone, anywhere (e.g. not just on the field of battle) without review or restraint from any other branch of government.
Identify anyone as a terrorist and hold them indefinitely without meaningful access to a trial and without any meaningful ability to dispute their identification as a terrorist. 
Surveil anyone, anywhere without any meaningful judicial review and with the legal right to prevent anyone who learns of surveillance to tell anyone else about it upon pain of imprisonment. 
Kidnap anyone, anywhere and hand them over to foreign governments known to torture (of course the U.S. is also known to torture, see water Boarding, stress positions, sleep deprivation, solitary confinement, etc.) without any chance for legal review.
Also note, although it shouldn't matter, that all of the previous applies as much to U.S. Citizens as to foreign nationals.
The list above seems to me to be the very definition of 'unrestrained exercise of power'.
I know it seems down right odd to call a country where you can post an article like this and not immediately go to jail a tyranny. But that is a fake freedom. I'm allowed to post these things because I'm a white adult reasonably well off male, part of the power class. So these kinds of posts are seen as 'cute' or 'liberal' or some other harmless word. No one in the government is likely to take them seriously. Until, of course, they do. So far that hasn't happened so I judge myself reasonably safe in posting them. We largely limit our tyranny to brown and black people and poor whites, these are the unpeople so generally the government feels safe doing just about anything they can think of to them.
But here's the bottom line, today a single person, without any meaningful checks or balances, can within the bounds of accepted law and practice kill, imprison, kidnap or surveil anyone, anywhere. That seems to me to be a pretty text book case of tyranny.
 The president attached a signing statement to NDAA claiming that he wouldn't use his powers against U.S. citizens but we should be clear that this is irrelevant, everyone has fundamental rights, not just U.S. citizens and that the legal restraint of a signing statement is pretty much nil. The president can change his mind at any time and of course the statement has no bearing on his successors. So as a practical matter his signing statement is quite literally irrelevant.
 For example, right now 46 people are sitting in Guantanamo Bay who the U.S. says are terrorists but doesn't believe it has enough evidence to prove this and so intends to jail them until they die. If nothing else in this article makes you think I hope that one does. There are 46 people who the government refuses to charge and yet intends to hold for life.
 In theory the President is supposed to put his requests for surveillance through the FISA court. In practice President Bush couldn't be bothered in a number of cases and the other 'branches' of government just rolled over. Also note that the FISA court is only required to approve in retrospect (e.g. Surveillance can begin before approval is sought) and that between 2000 - 2010 out of 30,000+ applications only 11 were rejected and those were apparently all re-submitted with unknown modifications and approved. With those kind of numbers I think it's pretty fair to say the FISA court is toothless. And again, this depends on when the President even bothers to put something through FISA, which Bush was clear he didn't think he had to do. To give a sense of how many people are involved the government estimates that between 2005 - 2010 142,850 people were under surveillance via FISA. But we already know that in practice the number of being put under surveillance is vastly higher.