Immigrants can still find success in the United States. Many immigrants come to the US already degreed and with skills in hand. For these poeple, success is almost imminent. Other immigrants will need to work much harder, get an education or trade training, and wait for years. It is all very possible though.
I believe it is easier for an immigrant to find success in this country than it is a natural citizen. Immigrants entering the United States often have a support group of friends and family already here and well established. They band together to support one another and provide a strong start for new arrivals. Immigrants are also usually willing to work extremely long hours in the effort to establish themselves and become successful.
Yes they have more opportunities than most Americans do now a days. They are becoming the majority and the people that live here are becoming a minority in this country. This country is putting the African Americans in Prisons, they are sending the whites to war over in Iraq and killing off everyone but the immigrants. History is repeating its self.
Despite its being described as a "melting-pot", the United States has irrefutably gone through some xenophobic phases, and there is still a strong sense of cultural identity among most people who would call themselves "Americans". Nevertheless, one of the great things about this nation is that success is only a matter of effort, and anyone, whether natural-born citizens or immigrants, can find it if they are willing to put in the effort necessary.
America remains a land of opportunity and many people can still find success there. America still has the world's largest economy, and some of the best living conditions of the world. People can also find political and religious freedom in America which might be lacking in the countries they came from.