America traditionally (and still to this day) has a low population density. This means lots of land and not a lot of people living on the land. Much of the land in America is very fertile and suitable for farming. So, post-discovery of the Americas and with the exception of the very first settlers (Jamestown, for instance), farming the land and acquiring food hasn't really ever been a problem since there is just so much arable land and so few people. Even today the population density of the US isn't all that high (35 people per sq km). What's helped the US even more is that, when compared to the rest of the world, it has been governed quite well and has had a very strong economy since it's foundation.

In terms of food production and famine-avoidance, the US basically has every advantage one could ever want.

For much of the 1800s, wages in American cities were much higher than their European counterparts, for the reason that there was so much free land, were wages not that high, people would have simply reverted to farming. America is one of the few nations that could probably feed itself, along with the Ukraine and Russia, to give some other prominent examples (this is current, I'm sure if the situation dictated, some other countries could invest in agriculture and become self-sustaining, but not as many as you might think).

A main period of trouble was during the Great Depression, but this was largely malnutrition, rather than famine. This article has some facts on it, but while millions were hungry, actual cases of death from starvation were rare:

"President Herbert Hoover declared, "Nobody is actually starving. The hoboes are better fed than they have ever been." But in New York City in 1931, there were 20 known cases of starvation; in 1934, there were 110 deaths caused by hunger. There were so many accounts of people starving in New York that the West African nation of Cameroon sent $3.77 in relief."

There's also this guy who seems to believe that America lost 2 million people+ in the famine of the 1930s. Make of that what you will, but it seems inordinately high (especially given the generous relief efforts of the Cameroonians), and a quick read through makes it look like some of his arguments are very shaky.

Wasn't the Dust Bowl a large starvation event?

I have a follow up question to OP's, (if this is allowed in top-level comments. If not, please let me know).

In an International Studies course I recently took, my professor said that there have been no large-scale famines in democratic countries, and that the largest scale famines took place in authoritarian, communist regimes (eg. the Five-Year Plan in Mao's China). Such famines can be blamed on lack of civil liberties such as freedom of press, and the lack of an ability to hold officials accountable since they are not elected.

Is this an accurate claim and is this a factor in OP's question?

There are also claims that during the Depression of 1932/1933 malnourishment was a commonplace. For example, Russian historian Boris Borisov in his article "The Great American Holodomor" (avaliable in Russian http://novchronic.ru/1322.htm) used similar statistic methods used for counting the victims of Ukranian Holodomor and came to conclusion that US lost 7,367K lives due to famine.

The implicit scope of the article was actually to show that the notion of Holodomor was politically driven and the statistic methods used in the researches of Holodomor are unsustainable and can also be used to demonstrate severe famine in the US, but still there is opinion that US came close to starvation during The great depression.

What about for First Nations people before/during European conquest?