Thursday's White House meeting with Democratic Gov. Andrew Cuomo of New York and Republican Gov. Chris Christie of New Jersey also included several members of the two states' Congressional delegations.
Democratic U.S. Sen. Charles Schumer says that while no decisions were made, officials from the two states made a strong pitch for the project.
The $13 billion project also involves renovating the existing century-old rail tunnel connecting New Jersey and New York City.
Project supporters hope the Republican president honors Democratic former President Barack Obama's pledge that the federal government would pay for half the project.