The US president has the power to unilaterally order a nuclear strike on any point on the planet at any time they choose, regardless of how anyone in the other branches feel about it at the time. So 'limited,' maybe, but also able to end life on Earth as we know it on a whim.

That's an aside, however. I'm talking about the general concept of an executive office, not specifically the US president. And sure, there can be limits, but the whole point of an executive is to avoid endless deliberation in the appropriate situations. Perfect example: Congress had the constitutional power to manage tariffs, and they surrendered that power to the president willingly because they weren't able to be decisive enough with it.