WASHINGTON—Senate Democrats held up the confirmation of three top Transportation Department nominees this week, including two deputies to Secretary Elaine Chao, in a dispute over a proposal to build a new Amtrak tunnel between New Jersey and New York City.

The four senators from New York and New Jersey, including Minority Leader Chuck Schumer (D., N.Y.), say they delayed the nominees out of concern that the administration is uninterested in pushing ahead with a new tunnel under the Hudson River—and might ultimately decline...