This isn't quite true anymore. Over the last 2 centuries the President has little-by-little become more like a King. What I mean by that is that he has gained more powers that an absolute authority, like a King, would have. For example, the President has the power to write executive orders, which have the effect of law.
While true that these orders can be challenged by congress, they normally aren't likely due to human nature (it's easier to say no to an idea than to stop somebody who has momentum). The end result of this is that the President now has the power to basically write laws. If he is not happy with Congress's opinion, he can take matters into his own hands. On most issues he gives deference to the law-making body's authority, but the power is always in his hands to act; in other words politically and practically he is held in check on most issues by Congress and is obviously not a King (ie he can't act unilaterally), but as time passes he gets more of the power that a King would have.
While true that these orders can be challenged by congress, they normally aren't likely due to human nature (it's easier to say no to an idea than to stop somebody who has momentum). The end result of this is that the President now has the power to basically write laws. If he is not happy with Congress's opinion, he can take matters into his own hands. On most issues he gives deference to the law-making body's authority, but the power is always in his hands to act; in other words politically and practically he is held in check on most issues by Congress and is obviously not a King (ie he can't act unilaterally), but as time passes he gets more of the power that a King would have.
Edited for clarity