In the Democratic race, Hillary Clinton was hoping her own expected home-state victory in New York will help her recapture momentum from U.S. Senator Bernie Sanders of Vermont and cement her lead.
Paul Manafort, who is in charge of running Trump's strategy to amass delegates, met with lawmakers from the U.S. House of Representatives, including with some who have not endorsed him but may be considering it, according to those present. Manafort was expected to hold a similar gathering with some lawmakers from the U.S. Senate later on Tuesday.
Manafort "feels that there are four or five different pathways to 1,237," Congressman Scott Desjarlais of Tennessee said, referring to the number of delegates a candidate needs to secure the Republican nomination for the Nov. 8 election.
Trump, front-runner for months in the Republican race, currently has 744 delegates, while U.S. Senator Ted Cruz has 559 and Ohio Governor John Kasich is trailing far behind with 144, according to an Associated Press count.
If Trump does not secure enough delegates needed to win the Republican nomination outright at party's July convention in Cleveland, delegates would be allowed to switch to another candidate.
Opinion polls show Trump has a double-digit lead in New York, where the "winner takes most" primary carries 95 delegates. But a big win for Trump in the state York would not erase his vulnerabilities.
Cruz's skillful use of party rules during the primary process has angered the New York billionaire, who says the system is rigged against him. Trump remains unpopular with the Republican leaders and activists who select and serve as delegates, whereas Cruz has invested time and money courting them.
Some establishment Republicans have been alienated by Trump's more incendiary proposals, such as building a wall along the border with Mexico and slapping a temporary ban on Muslims entering the country. Others see the former reality TV star as an interloper who has not courted them and who has run his campaign in the national media.
Trump has sought to mend fences with the recent addition of veteran political strategists such as Manafort and Rick Wiley, who will take the lead in upcoming nominating contests, according to a Republican source familiar with the campaign's operations.
Congressman Lou Barletta of Pennsylvania said Manafort told House lawmakers the Trump campaign has an "open door."
"It is good that they are reaching out to members here, to get policy ideas, and bounce ideas off," said Barletta, who has endorsed Trump.
While Trump has muted his threats about unrest if he is denied the nomination at the Cleveland convention, his campaign's steady criticism of the nomination process has put the Republican National Committee on the defensive.
RNC Chairman Reince Priebus met with congressional Republicans in Washington on Tuesday to explain to them how committees and delegates are chosen for the convention and how it will be organized, House of Representative speaker Paul Ryan said after the meeting.
"He is making sure that the rules are the rules, and we follow the rules,” Ryan said at a news conference.
Opinion polls put Clinton ahead of Sanders in New York, which has been the scene of some of the harshest exchanges between the two Democrats. Clinton represented New York for two terms in the U.S. Senate, while Sanders was born and raised in Brooklyn.
Clinton has 1,758 of the 2,383 delegates needed to win the Democratic nomination to Sanders' 1,076 delegates, according to an Associated Press tally. A total of 291 delegates are up for grabs in New York, and a big Clinton win there could make her delegate lead insurmountable.
In Democratic nominating contests, pledged delegates are awarded proportionate to the support a candidate receives in each state, while super delegates, who make up a smaller proportion, can support any candidate.
"Any double-digit win would really reassure everybody that the (Clinton) campaign is reaching the voters who are going to be the people in November that are going to carry her to victory," said Dan Fass, a longtime Democratic donor in Rye, New York.
The former secretary of state had a message of unity as she made a last appeal for New Yorkers' votes, speaking on Tuesday at the North America's Building Trades Unions annual legislative conference in Washington.
Clinton recalled how when she was a U.S. senator, she immediately returned to Manhattan after the Sept. 11 attacks to survey the destroyed World Trade Center with fellow U.S. Senator Chuck Schumer of New York, a Democrat, along with the city's then-mayor and state's then-governor, both Republicans.
"Our next president will also face the test of bringing people together. After this campaign with so much ugly divisive rhetoric we’re gong to need some unity," Clinton said.
Clinton promised that if elected president a cross made by an ironworker from World Trade Center wreckage would hang in the Oval Office as a daily reminder of her commitment to workers.