This is an interesting question.
We have to think of the German jews at first, as the pressure on the increases right in 1933 and becomes unbearable by late 1938. OTL, due to this long escalation during peacetime, a good deal of them could escape Germany at least at first (notable example for false security: the Frank family in Amsterdam) - however going for any place they can reach. An "open" US would quickly become the preferred destination (Palestine / later Israel might suffer to that regards).
There were 500,000 German jews. OTL, about half of them had emigrated by the outbreak of the war. The decision not to emigrate was generally a tragic mistake. However- even with faciliated access, some people just would not be ready to leave. Too old, too sick- or bound to old and sick relatives. Too patriotic and unwilling to leave German culture behind, unwilling to start a new life and profession, the vain hope that Nazism might just go away or not end up enacting unthinkable cruelties... and then there is the fact that the Nazis abused Weimar legislation to ensure that whoever escapes the 3rd Reich....does so with only a fraction of his money (Reichsfluchtsteuer).
Ironically, NS authorities would joyfully co-operate with US organisations. Because, as long as war and dominance over (Eastern) Europe was not in the cards, making jews emigrate seemed to be the only feasible way to get rid of them. However, as soon as the 2nd World War starts, I see the logistics of migration to become too tough for any massive movements. Even if you still had charitable organisations organizing the flight of Jews, their work would have become extremely difficult.
So let us assume that a friendly US legislation increases the willingness of Germany's jews to board a ship, I expect that at least a quarter of them remains in the homeland no matter what. Instead of 250,000 , about 375,000 leave - but most of them to the United States. Let us say, 85%.
So we talk about little more than 325,000 persons over the course of seven years (1933-39). Basically, New York City could swallow them up. To be honest, I do not see any actual settlement projects apart from a few quasi-Zionist projects. Why should the United States treat them like Native Americans and basically relegate them to reservations? Very few of these immigrants would be used to living on the countryside. Their professional expertise would make them seek employment in the metropolises of the CONUS.
***
In 1938/39 we can add numbers some by including Austria, then the Czech Republic, into the addition. The general situation would however be the same. Readiness to leave Austria, where the "frog in hot water effect" didn't occur, but Nazis terror reached Vienna (where almost 90% of Austria's jews lived) overnight with full force, seemed to be higher. 120,000 of a bit more than 200,000 could emigrate within less than two years.
So that makes a realistic number of 150,000.
In the Czech Protectorate, only 26,000 of 120,000 Jews could flee. Here we could see a significant increase, optimistically perhaps to 80,000. Don't forget: the window of opportunity here (after March 15th, 1939) is very narror!
Given the time pressure, the US are the destination of 90% of these refugeees. So we add ca. 210.000 people to 325.000 .... 535.000.
***
Now here is a big question. What does the legistlation making an exception from the quota system of the day look like? Does it only refer to immigration from the Reich? Because then we talk about exactly these three numbers above.
Or does it mean that Jews can come to America no matter what or no matter where from? Frankly, I would assume that to be a hot political topic. Would Tevje be as welcome as Albert Einstein?
IMHO, a legislation which allows a substantial number of Eastern European Jews to flee before Wehrmacht, SS and Einsatzgruppen overrun their home (and afterwards, it is too late for saving more than a few - remember, about half of the Holocaust has already been done before the extermination camps opened their gates) is only feasible in a scenario when the tightening of US immigration laws in the 1920s either a) doesn't happen or b) gets strongly scaled down / aboslished at the start of FDR's presidency.
This, however, would let a lot of the trends of the 1900s and early 1910s continue: a generally strong immigration, increasingly from Eastern and Southern Europe... not just Jews. Leaving the Soviet Union would prove difficult (though it doesn't seem to have been absolutely impossible), so if such a measure saves European Jews, we mainly talk about Polish, Rumanians, Hungarians.
So, the earlier immigration restrictions get lifted, the less Jews the Nazis will find in Eastern Europe. But I agree that it is hard to imagine the combined numbers of 1933-1945 Jewish immigration rise above 1,000,000.