You often hear people describing somebody's accent as "American". Truth is, there isn't a single American accent. There are regional accents that vary as you go across the United States.
The most distinctive ones are probably the New England and Southern accents. The New England dialect includes dropped Rs and extra Rs at the end of words that end with vowels. The "A" is pronounced as ah. The result being "Pahk the cah in Hahvuhd Yahd" (Park the car in Harvard Yard). Southerners, on the other hand, tend to speak slower, and thus create the famous southern drawl. They pronounce "I" as ahand "OO" as yoo. The result being, "Ah'm dyoo home at fahv o'clock." (I'm due home at five o' clock).
The funny thing with American accents is that everybody wants one. Think of all the Indians who go there to study or work. They come back on visits with gifts and an entirely new way of speaking. The accent takes time to reach perfection, but almost every Indian in America makes sure that they have one. ABCDs are born with one, courtesy of being born on the US soil, but Indians from India need to work hard. I know of a South Indian graduate student who worked so hard that he lost his natural rolling Rs.
Then there are the people working at Indian call centres. Most of them have to go through an intensive process called accent training so that they can get that American accent. This training has become necessary with American customers complaints about desi diction. Sometimes, they just don't understand the call centre executive. Other times, the accent just seems plain funny to them and they would rather be speaking to a person who talks like them.
I've noticed that my Chinese friends in America (the Chinese from China) don't work too hard on their accents. I can't blame them. Chinese languages are so different from English, that switching over to an American accent can be a daunting task. Then I look at the Indian community there, and everybody, including people old enough to be my grandparents, has that American twang!
But honestly, is the most sought after accent really necessary for survival? Probably not. Intelligent Americans can understand you as long as you speak clearly and with proper diction. There is also a minority group of Indians who do not try to change their accent. Most of them survive just fine. There is no need to struggle for this. Just remind yourself, Penelope Cruz never lost her Hispanic accent, but the Americans love her!