The deadline to change your party affiliation in time for the June primary election is motzei Shabbat at 11:59 pm. You can do it online.
Jewish advocacy organization are urging voters in New York City to be sure they are registered as Democrats so they can vote in primary contests that may be contested by radical candidates whose positions conflict with those of the Jewish community.
Being a registered Republican or independent in NYC is like not voting, since the Democratic primary in NYC typically decides the election. You can change your party again after the primary.