Actually, the peak of immigration to Brazil was during the Republic - 1 million alone during the 1904-13 period. There's a lot of reasons for the reduced immigration compared to the USA, some of them even mentioned here:
- It was cheaper to immigrate to the US: not only due to the distance; some countries(Germany mainly, in the 1860-70's, but also Italy from 1903 on) only allowed unsponsored immigration(that is, the immigrants had to pay for their passage) to Brazil. This was,at least in Germany, due to (true)reports of mistreatment of the immigrants who were sponsored by Brazilian landowners(who were used to dealing with slave labour) in the 1840's and 50's. The Imperial government later offered other incentives for German immigration that didn't fall on the sponsored immigration category, but German immigration never quite recovered;
- It was easier to acquire land on the US: while the USA had the Homestead Act, which ensured cheap, or even free, land for immigrants, the Brazilian Lei de Terras(1850) stated that from then on, with the exception of a strip 10 leagues(66 km) wide from the Brazilian border, land could only be purchased. This meant that land ownership was beyond most immigrants. While there were people who acquired land on auction, divided them in terrain lots, and sold to immigrants, most immigrants who came to Brazil did so as labour for landowners(the Lei de Terras was approved 2 weeks after the law which forbade slave trafficking, and was designed to ensure immigrants wouldn't mostly become homesteaders);
- Brazilian climate(and the diseases associated with it) was hard on Europeans: not only for those who went on to the interior of the country; Rio de Janeiro had the charming nickname of "graveyard of the Europeans". It was better to immigrate to the US, or Argentina and Uruguai, than to a country where conditions had similarities to India and subsaharian Africa;
- There isn't that much fertile land in Brazil: this is a minor factor, because when immigration was at its apex, the frontier was where there was fertile land for planting(the "terra roxa" volcanic soil on western São Paulo and parts of Paraná State). Even then, a lot of Brazil was left sparsely settled until the 1970's, when EMBRAPA figured out how to deal with the acidic soils of the Center-West region. Until then, while there were some agricultural colonies in the 1930-40's, and Brasília was founded in 1960, most of that area was suitable only for extensive cattle-raising, and therefore not suitable for colonizing.