Exponential growth starts with some number, and our starting number is probably larger than theirs, because we have more people to begin with, so more of our citizens returning from elsewhere probably had the virus. Similarly, our upper bound is significantly larger; we can double our number of cases 2-3 times more than a lot of other countries can.
Think about a hypothetical country with 100,000 people. For them, 14k is 14% of their population. That is going to happen about the same point in their curve that 14% of the population would take in our curve, because we've got many more people in many more different cities, etcetera.
So, basically: Don't think "starting from 1, how long does it take to get to 14k". Think "starting from 1-in-a-million, how long does it take to get to 14k". So for Italy, that'd be 60 to 14k, and for the US, it'd be 330 to 14k, which is to say, we're earlier in the curve.
How many people at once do you think can be taken care of by hospitals for a given population size, usually?
Italy tends to about 3ish hospital beds per 1k population, the US to a bit lower. But of course, some of those are already in use; estimates look like rough order of about half a free bed per 1k population, but they only have about half as many ICU slots per capita as we do. So in theory Italy as a whole might have, say, about 30k hospital beds available, for 60M population, while we have similar-ish numbers per capita, but about 330M people, so we have probably about 160k available beds. So 14k would be about half of all their theoretically available beds, and that means that a lot of specific places are badly overflowing already, while 14k here would be a much smaller proportion... so far. In the last day, the source I checked showed us with 8k new cases, Italy with 5k new cases. They're at about 60k total, we're only at about 32k, but we'll run past them, easily, in total numbers. (Consider: If we keep it to 20% of our population, that will be more cases than if 100% of their population got sick.)
