With Michael Dukakis again holding the upper hand, the Democratic presidential candidates descended full force on New York today for a two-week run to the crucial April 19 primary. Dukakis picked up back-to-back wins in Colorado and Wisconsin this week over Jesse Jackson, to follow up on home turf victory in Connecticut. Before that, Jackson had piled up victories in Michigan and Illinois. Even before the polls closed in Tuesday's Wiscnsin contest, Dukakis and Tennessee Sen. Albert Gore Jr. were prospecting in New York, hoping to stake a claim on the mother lode of the primary season thus far. ``I hope it's a sign of things to come,'' Dukakis of his Wisconsin win. Jackson, too, was upbeat abut his prospects. ``We go to New York with a good campaign, a broad-based campaign, momentum, a clear messge _ a message that applies to New York,'' he said Tuesday night. At stake in the New York primary are 255 delegates. At the national convention, only California's delegation, a 336-member giant, will be larger. And that primary isn't until June 7. ``We think that if we can win New York, we're going to be in a good position to dominate the last third of the primaries,'' said Paul Bograd, Dukakis' New York campaign manager. ``But New York will be critical to that.'' ``No way you can underestimate the importance of this one,'' said John Marino, executive director of the state Democratic Committee and a political operative of Gov. Mario Cuomo. Cuomo's presence is felt in the New York primary race, as it has been to some extent in the entire campaign. Reluctant to run for president himself, Cuomo has been equally reluctant to endorse any other Democrat. Cuomo's apparent indecision has fueled speculation for months that he might want a deadlocked convention and desperate Democrats turning to him offering the nomination. Cuomo has insisted he doesn't want that, but thus far has refused to rule out accepting a convention draft. There is also a Republican primary on April 19 in New York, with 102 delegates at stake. But it is little more than a formality as Vice President George Bush rolls toward the GOP nomination. On the other hand, the Democratic primary could provide important answers, including: _Can Dukakis keep up the momentum he's regained with this week's victories in Wisconsin and Colorado _ and convince party leaders that he deserves the nomination? _Can Jackson's solid support among minority voters and the backing of several prominent New York labor leaders overcome Jewish uneasiness and produce the New York victory his campaign now needs? _Will Gore's decision to put most of his remaining eggs in the New York basket prove to be anything more than a windfall for television stations who run his paid ads? Along with Cuomo, most of the state's other major Democrats, such as New York City Mayor Edward Koch and Sen. Daniel Patrick Moynihan, have remained officially neutral. Recent polls among New York Democrats have Dukakis leading the field with support ranging from 37 percent to 45 percent, depending on the poll. Jackson has been consistently second at just under 30 percent while Gore and Simon have yet to crack double digits in any of the polls. Anticipating Dukakis' victory in Wisconsin, Bograd declared Tuesday evening that the campaign had become ``clearly a two-man race'' between Dukakis and Jackson. While the Dukakis camp was ready to write off Gore, who finished a distant third in Wisconsin, the Tennessee senator has been campaigning hard here for more than a week. He's also hired New York political consultant David Garth, who runs Koch's campaigns and who occasionally advises Cuomo. Gore has been courting New York's politically important Jewish community, and has been attacking Jackson and Dukakis on the issue of support for Israel. If that message has any impact it could hurt Dukakis most; Jackson's support among New York Jews is already minimal following his 1984 ``Hymietown'' gaffe. However, Dukakis' wife Kitty, who is Jewish, has been campaigning in the Jewish community. Jackson is relying on his strong minority support, coupled with a growing acceptance among white voters, to win more than the 26 percent he garnered in the New York primary four years ago. Jackson plans a big television buy in New York, a tool he hasn't used much in other states. He also has the support of influential labor leaders such as Stanley Hill, executive director of the 120,000-member New York City municipal workers union, and Jan Pierce, a top official with the Communications Workers of America. Bograd, Dukakis' New York campaign manager, says the Massachusetts governor will spend at least $1 million on his New York effort; others put it as high as $3 million. The Massachusetts governor also has the support of some of the top officials from the state's politically powerful teachers' unions.