Bradbury's The Martian Chronicles is a tale of conquest drawing many parallels with the invasion of America. Just as Europeans came to America and imposed their rules and customs nearly exterminating the natives in the process, so the humans came to Mars and did the same. The parallel is most obvious in "—And the Moon Be Still as Bright" where Spender talks of Cortes' destruction of the Aztec Empire and Cheroke shows empathy for the Martians because of his Cherokee ancestry.
"The Shore" describes the beginning of colonization. "The first wave carried with it men accustomed to spaces and coldness and being alone... Everyone knew who the first women would be." Reading these words it's easy to imagine some Wild West frontier town populated by men and women of dubious moral. In the stories like the "Interim" and "The Martian" towns grow more akin to those of Bradbury's time, showing the human community on Mars evolving just like its older counterpart in America. But Bradbury doesn't stop there. He presents a future of the colonizers and it isn't bright.
People came to Mars for various reasons but they all looked at it as a chance for a better life. Just as they did coming to America not so long ago, and even still do. Interesting thing is that the Mars invaders are exclusively Americans, which indicates they are the descendants of those who made the similar invasion few hundred years ago and further strengthens the idea of Mars representing America.
Unfortunately, as Bradbury shows at the end of "The Naming of Names", the land of opportunity soon becomes bereft of it. Those who want to rule others catch up those who want to rule just themselves. But the ending of the Chronicles bears a spark of hope as the humans are given a second chance. It is what Bradbury wanted for America, a new start.