He won a big victory in Wisconsin. He pierced the Donald Trump mystique. He even got some of the Capitol Hill lawmakers who regard him as a revolutionary and renegade to slink cautiously into his corner. By all logic, this should be a Ted Cruz moment — if only the next primary weren’t in New York.

But in two days New Yorkers go to their polling places, and though Mr. Cruz has been the beneficiary of the calendar before — his performance on Super Tuesday helped force out of the race Sen. Marco Rubio of Florida, a demographically identical and philosophically similar rival — his success still depends on another man to stumble.

Or — just as frustrating to a man with a sense of destiny and a fast-forward vocabulary of ambition and determination — his success requires another man to fail to stumble across the finish line represented by the figure 1,237, the number of delegates required to win the Republican presidential nomination in Cleveland this July.

And even if that other man — Manhattan businessman Donald J. Trump, as the whole world knows — fails to clinch the nomination as the last primary votes are cast June 14, when the District of Columbia’s tiny Republican minority goes to the polls, there is no guarantee that the remainder candidate, which is what Mr. Cruz is, would prevail in a contested or open convention.

All of which is why, though the cage fight between former Secretary of State Hillary Rodham Clinton and Sen. Bernie Sanders of Vermont is great sport, and perhaps precursor to an upset, the struggle between Mr. Trump and Mr. Cruz is more compelling.

“The focus of New York is on the Republicans, period,” Richard Ravitch, former head of the New York City transit system and a former Democratic lieutenant governor, said in a recent telephone conversation. “Bernie and Hillary are going to campaign, and they are going to fight, but it’s the Republican mashup that’s really worth watching.”

That’s because, for all unexpecteds in the Democratic race — no one on New Year’s Day thought a 74-year-old self-proclaimed Democratic socialist from a state with three electoral votes would defeat the mighty Clinton machine in Michigan and Wisconsin, states carried by Ms. Clinton’s husband Bill — the Republican race is a symphony of surprises.

The first of those surprises was that a candidate such as Mr. Trump would be a serious threat to win the GOP nomination. The second was that voters would tolerate torrents of invective and insult from a candidate for a position that Franklin Roosevelt, the president against whom modern presidents are measured, described as being primarily an office of moral leadership.

Now, as some powerful Republicans seek to deny Mr. Trump the party’s presidential nomination, some of the assumptions about Mr. Cruz are being challenged, especially the twin notions that the Texan could win no adherents among party leaders and that he has no ties to Republican thinkers and theorists.

In the event, Mr. Cruz has been Velcro to all manner of Republicans who agree with the notion that he is the only living soul who stands between Mr. Trump and the scene many Republicans dread the most: the real estate-and-casino tycoon standing with his arms raised high as balloons and confetti rain upon him in Cleveland.

Mr. Cruz, whose rhetorical repertoire includes the phrase “Washington cartel,” now has the support of increasing numbers of important GOP fundraisers. He has the allegiance not only of perhaps the most conservative lawmaker on Capitol Hill, Sen. Mike Lee of Utah, but also of, among others, former Gov. Jeb Bush of Florida and Sen. Lindsey Graham of South Carolina, who once suggested that deciding between Mr. Cruz and Mr. Trump was a Hobson’s choice. “Whether it’s death by being shot or poisoning doesn’t really matter,” he said.

In truth, Mr. Cruz has stronger relationships on the House side of the Capitol than he does on the Senate side, where he has toiled for about three years and, according to multiple accounts, set a Washington record for alienating his colleagues. But many of his Senate aides formerly worked in House offices and, in an example of how Washington works, they provide a bridge to their former bosses and their former colleagues.

Also, long before he formally entered the presidential race, or even before he mounted his 21-hour filibuster in 2013 against Obamacare, likely undertaken to attract attention from devout conservatives, Mr. Cruz began establishing himself as a moderator in forums designed to combat moderation in his party. These events, attended by Republican lawmakers and top staff, were convened to examine contemporary issues from a conservative viewpoint.

Now, those relationships — in some ways more important than ties within the Senate chamber — are bearing fruit, even as former Sen. Phil Gramm of Texas is launching a massive effort to pull in more senators, perhaps Sen. Tim Scott of South Carolina, the first African-American to be elected to both the House and the Senate and a conservative avatar, or Sen. Steve Daines, whose principal political attribute is that he represents Montana, which votes June 7 and could be important in blunting Mr. Trump’s drive to the nomination.

Of such things a convention majority might be built — or at least a wall against Mr. Trump. But first there is the New York primary.

Mr. Trump holds many if not all the cards. He was born in the state, reared in Queens and works and lives in a glittery Manhattan tower that bears his name. Not since early February has his advantage in New York state polls fallen below 26 points, flaring to 52 points a month ago but now cruising along at just over 30.

Yet Mr. Cruz is playing on a bigger field, trying to peel off first-ballot votes from delegates elected but not formally pledged, or strategizing to conduct guerrilla wars in state capitals, such as Bismarck, N.D., and Denver, Colo., where delegates are floating like uncharged molecules and might ultimately become, in the Cruz mold, free radicals.

So while the television cameras are on the outdoor game — rallies, street encounters, visits to ethnic enclaves and upstate urban centers — Mr. Cruz is playing the sort of indoor game where he has surprising strength. Ted Cruz might have his moment in Cleveland.