New York's electoral importance (again, 45+ Electoral Votes) is not going to disappear overnight. For a Democratic Party who's solid south base is showing signs of cracking, winning the state is paramount to the party's electoral fortunes, and same thing for the Republicans, Dewey could've flipped every close Midwestern state Truman won in 1948 and if he lost New York he'd still lose the election. In a close Presidential election, the Empire State is the ball game, and neither party can afford to write it off.
As for the others, the Supreme Court, chock full of Roosevelt appointees, isn't going to do anything about it. Congress is filling up with young Republicans and Democrats who just come back from fighting WWII, and an not unsubstantial amount who've toured the Nazi Concentration Camps which would've changed the viewpoint of all but the most vicious anti-semite, and the general public is enjoying peace and prosperity after the end of the turbulent post World War aftershocks.
If there's any time for large consensus that supports letting in Jewish refugees, you could do worse then the era after the 2nd World War, and again several decades, that's important. 3,500,000 people across ~20 years is 175,000 people per year, it's about what the US set the yearly quota for refugees in 1980, it's hardly unimaginable.