Ben Fractenberg/THE CITY A coalition of good government and business groups is calling on Gov. Andrew Cuomo to extend the deadline for voters to change their political party to until less than a month before the city’s June 22 citywide primary elections. Supporters of moving the already-passed deadline to May 28 say it would help more voters participate in the crowded upcoming mayoral race and other contests dominated by Democrats. But some Democrats see the bid as a distraction at best and at worst as an incursion that could have outsiders dipping in and swaying party primaries. Altogether, some 3.3 million voters are registered as Democrats in the city, compared to 1.6 million New Yorkers who are with other parties or unaffiliated.