President Trump’s promise to enact a sweeping overhaul of the tax code is in serious jeopardy nearly 100 days into his tenure, and his refusal to release his own tax returns is emerging as a central hurdle to another faltering campaign promise. As procrastinators rushed to file their tax returns by Tuesday, the White House press secretary, Sean Spicer, emphasized again on Monday that Mr. Trump had no intention of making his public. Democrats have seized on that decision, uniting around a pledge not to cooperate on any rewriting of the tax code unless they know specifically how that revision would benefit the billionaire president and his family. And a growing roster of more than a dozen Republican lawmakers now say Mr. Trump should release them. “If he doesn’t release his returns, it is going to make it much more difficult to get tax reform done,” said Senator Chuck Schumer, the Democratic leader, pointing out that the president has significant conflicts of interest on issues such as taxation of the real estate industry and elimination of the estate tax. “It’s in his own self-interest.” It’s interesting that even though all agree the tax code needs to be reformed, it is more important that a single person’s return be seen. A… With Republicans sharply divided on a path forward and the administration unable to come up with a plan of its own, the Democratic resistance is only the newest impediment. As a candidate, Mr. Trump declared that he understood America’s complex tax laws “better than anyone who has ever run for president” and that he alone could fix them. But it is becoming increasingly unlikely that there will be a simpler system, or even lower tax rates, this time next year. The Trump administration’s tax plan, promised in February, has yet to materialize; a House Republican plan has bogged down, taking as much fire from conservatives as liberals; and on Monday, Treasury Secretary Steven Mnuchin told The Financial Times that the administration’s goal of getting a tax plan signed by August was “not realistic at this point.” A tax overhaul could be the next expansive Trump campaign promise that falters before it even gathered much steam. “If they have no plan, they can’t negotiate,” said Larry Kudlow, the economist who helped Mr. Trump devise his campaign tax plan. “In that case, tax reform is dead.” The first pitfall for Mr. Trump was the debacle of his health care plan, which burned political capital and precious days off the legislative calendar. But his administration saw repealing the taxes imposed by the Affordable Care Act as an important step that would allow for deeper tax cuts later. Mr. Trump even suggested last week that he might return to health care before tax cuts. Republican leaders in Congress also failed to create momentum. Speaker Paul D. Ryan built a tax blueprint around a “border adjustment” tax that would have imposed a steep levy on imports, hoping to encourage domestic manufacturing while raising revenue that could be used to lower overall tax rates. But it has been assailed by retailers, oil companies and the billionaire Koch brothers. With no palpable support in the Senate, its prospects appear to be nearly dead. Heading into a congressional recess, Mr. Ryan admitted that Republicans in the House, Senate and White House were not on the same page. The president’s own vision for a new tax system is muddled at best. In the past few months, he has called for taxing companies that move operations abroad, waffled on the border tax and, last week, called for a “reciprocal” tax that would match the import taxes other countries impose on the United States. But it is Mr. Trump’s own taxes that have provided the crucial leverage for his opponents. More than 100,000 of his critics took to the streets over the weekend in marches around the country, demanding that the president release his returns. Tax legislation, they say, could be a plot by Mr. Trump to get even richer. “When they talk about tax reform, are they talking about cutting Donald Trump’s taxes by millions of dollars a year?” asked Ezra Levin, a member of the Tax March executive committee. “We don’t know.” Beyond the politics of Mr. Trump’s returns, lawmakers do not want to pass an overhaul of the tax code that unwittingly enriches the commander in chief and his progeny. Those who are worried about conflicts of interest point to the potential repeal of the estate tax or elimination of the alternative minimum tax as provisions that would enrich Mr. Trump. Perhaps the most consequential concern relates to a House Republican proposal to get rid of a rule that lets companies write off the interest they pay on loans – a move real estate developers and Mr. Trump vehemently oppose. Doing so would raise $1 trillion in revenue and reduce the appeal of one of Mr. Trump’s favorite business tools: debt. In the halls of Congress, Democrats are employing procedural maneuvers to drive home their point on the tax returns and possibly compel Republican lawmakers to join their effort to force Mr. Trump to release them. And Democratic aides say more tricks are coming. More than a dozen Republicans – from recognizable names like Senator Joni Ernst of Iowa and Representative Mark Sanford of South Carolina to backbenchers like Representatives David Young of Iowa, Matt Gaetz of Florida, Walter B. Jones of North Carolina, Ted Yoho of Florida, Rodney Frelinghuysen of New Jersey and Justin Amash of Michigan – have agreed that Mr. Trump should release his returns.