An uber generalization of Europe's reaction to the creation of the US, as I understand it, was "Wow someone finally stuck it to England." And then eventually, as America expanded and industrialized, it became a "land of opportunity" in the eyes of disenfranchised Europeans. To someone from Europe trying to immigrate to the US at that time I'm sure it made sense. America was mostly European, especially on the East coast, and most knew they could find a community in almost every major city.
Which makes me curious about people from Asian countries coming over in large numbers. They must have known that even in those "large" numbers they will be overwhelmingly a minority when compared to the rest of the population. When you factor in that much of Europe immigrated to the East coast full of big cities and hopefully much opportunity, it further makes me inquire why there was such a large influx of Asian immigrants, particularly when they were entering the country on the Western side: the "wild" one that was much more sparsely populated and had tougher living conditions than that of the East.
So while I think I have an understanding of Europe's reaction to, and opinion of, the US which would lead to high immigration figures (and if I'm wrong please correct me as brutally as possible) I have no understanding of what people thought about us and what our appeal was on the other side of the Pacific Ocean. Any insight on this is greatly appreciated.
While I am sure that someone will be able to answer this much better than I will, for short gaps during the 1840s and 1870s there was actually a little bit of encouragement by the governments of the US and California for Chinese to emigrate, but in almost every case these actions were quickly overturned for more and more restrictive measures, however some countries were less effected than others, Japanese immigrants in particular were given more chances to immigrate than other nationalities until the 1930s. The Philippines also generally had different rules pertaining to their immigration to the US due to their status as a US territory.
The main problem is that Asian is a broad group which often times had different rules affecting different groups, even the "Asiatic barred zone" in the Immigration Act of 1917 bars Georgia which is often considered European today, but leaves Japan and parts of China(which were already affected by the Chinese Exclusion Act of 1882) completely unaffected.
Realistically Asian, by any definition of the term, immigration to the United States was not realistically a possibility for the vast majority of Asians until 1968, when the Immigration act of 1965 went into effect. Demographically this is actually quite easy to see, the US from 1870 until 1950 maintained an Asian population making up 0.2% of the total population of the United States, not counting for more than 1,000,000 people until the 1960s. Today this less than homogenous group makes up approximately 5% of the US population, with more than 15 million people claiming Asian descent.