The big problem is the generally urban and professional makeup of the western Jewish population vs. the Agrarian nature of the USA, particularly the lands in the west that were open for the creation of new states.
I guess you need to have Russia turn even more anti-Jewish than OTL and force the Jews out wholesale, and then have most of Europe likewise prove hostile.
Perhaps some established wealthy Jews from the US could decide to stump up the cash to bring over the eastern european Jews and bribe enough politicians to let it happen (the latter is the hardpoint)
Don't forget that at the time, there were large quantities of Jews (mostly in Russia) living on shtetls, living agriculturally (mostly through near-subsistence farming). Think Fiddler on the Roof.
The problem is that these rural Jews were less likely to leave than the urban Jews for any number of reasons (less wealthy, more connected to their communities, more conservative...). Those that did came largely after the more urban Jews, and so they came to New York to find an already thriving Jewish community, and were hesitant to try their luck elsewhere.
We just need something to break this status quo. Maybe the German Jews in New York (that arrived decades before the Russian rabble) take measures to encourage them to pass on (either positively or negatively). Maybe the city or State of New York doesn't like absorbing all those Jews and takes measures. Maybe a state further west has some sort of economic incentive. And it won't take much - once a pattern of Jews arriving and flowing west is established, it'll continue.
Maybe something like this occurs: Wyoming is a very underpopulated state. It's cold, yes, but not much colder than the Pale. The soil is fine for farming and ranching (Ukrainians settled in the Canadian prairie did very well). And Wyoming has shown a willingness to entertain unconventional means to increase their population in the past (they were the first state to give women the vote, largely it is thought to encourage women to immigrate.
And the 1900 population of Wyoming is 92,000, compared with 1.5 million Jews! So let's say that Wyoming (or Montana, or Idaho, or maybe even Alaska, but probably not Colorado) invites a smallish group Jews over in order to get some more people. They flourish, drawing more and more. This all starts about 1880 (Wyoming population: 20,000), which is when the Jewish immigration to the States begins in earnest. Wyoming passes the 50,000 person threshold just before 1890 historically; here, it'll be around the same, but the state will already be about a third Jewish by then (OTL pop: 60,000; is it really that hard to get 2% of the US's Jews to head to Wyoming?) Like pulls like, and by 1920, Wyoming is a strong majority Jewish - maybe even as much as 3/4. English is spoken amongst children, but Yiddish is more common in Cheyenne than any other language. Some cowboys and Indians complain about it, but the Jews are Godly, hardworking neighbors, so there's not an enormous amount of room for complaint.
In parallel, Zionists are starting to become interested in the idea. Yes, there's already several kibbutzim and cities established - and Tel Aviv, who can forget! - but the British make it clear pretty quickly that they're not so interested. And there's the US, letting in all kinds of Jews, and Wyoming, where Jews are engaging in agriculture, working the land, riding horses (the Zionists had a huge hardon for horses, I don't know why), working mines, building steel mills...and a combination of British pressure and increasing Arab violence is enough for whole kibbutzim to uproot and move, funded by wealthy Jews in Europe and the US, and also sometimes even by themselves. Even a lot of Tel Avivis found themselves ill at ease in their houses, own just reoccupied after the expulsion by the Ottomans just 3 years earlier.
By 1933, we have well over half a million folks in Wyoming (OTL: about half that), about 80% Jewish; Jews and non-Jews mostly live separately, but mix pretty peacefully, even in Cheyenne after a few drinks. A lot of Zionists have come to Wyoming, too, and put in a little piss and vinegar, but the mostly traditional Jews already there don't enormously like them, and so the communities stay mostly separated. New York and Wyoming Jews are friendly, but each looks down on the other; the New Yorkers for the steppers' rural ways and "building Poland in Wyoming", the steppers for the New Yorkers living like rats in a filthy little urban cage.
The passage of the Nuremberg Laws sees an interesting reaction. Historically, the Slattery plan to settle Jewish refugees in Alaska failed due to a lack of Jewish support, and Alaskan opposition. The Jews were mostly concerned that a sudden influx of Jews would lead to antisemitism. Here, though, we've already had half a century of people decrying Jewish control of American land, and most Americans regard Wyoming about as they do Utah (which, especially in 1933, is far from well - but tolerable). Several hundred thousand Jews arrive in the period from 1933-1939 (the total number of Jews in Greater Germany in this period is a bit less than 600,000 - I'm not sure how many the US would actually allow to arrive, or how many Wyoming can support - though Nebraska supported a population of 1.4 million at the same time, and has similar conditions). Not all of the Jews end up in Wyoming, but most do, even though most are German-speaking, urban, often secular Jews (and so clash with the shtetlers). The Nazis never seriously consider transferring Jews to the US for the same reason they never really considered transferring them to Palestine; the US wouldn't have let more than a few hundred thousand in, anyway - though the half million or so Jewish DPs are let in after the war.
In 1950, the state of Wyoming stands with a mighty population of about 2 million, well over three quarters Jews. They are divided into German and Polish/Russian types, even today, with the former mostly busily developing little towns and cities (Cheyenne is well over half a million), and the latter mostly living the quiet country life as farmers and ranchers. Wyoming and New York Jews remain two distinct cultures, with the latter mostly unchanged and the former sharing much with OTL Israeli culture,though not quite so militant. There are about 6 million Jews in the US (compare 4.5 OTL), split about equally between Wyoming, New York, and "other". A few hundred thousand hardy Jews remain in the Hashemite Kingdom of Palestine, which stretches across both sides of the river Jordan; though Tel Aviv remains a vital city, Haifa will become Palestine's first city, with Tel Aviv remaining a cute little Jewish enclave, given limited self-government. Over the years, the Jewish population in Palestine will contract slightly, as young people constantly trickle off in the US.
Fuck, I should develop that properly.