WASHINGTON — Bolstered by a growing backlash to President Trump’s immigration order, Senate Democrats on Monday steeled themselves to slow the confirmation of cabinet nominees, dimming prospects for cooperation with the new White House.

But each Democratic demand for procedural minutiae and details on nominees’ stances on Mr. Trump’s travel ban illuminated an immutable fact: There is little Democrats can do to stop Republicans from ramming through both Mr. Trump’s cabinet and their policy agenda.

Senator Chuck Schumer of New York, the Democratic leader, set the tone as lawmakers straggled back to Washington from a weekend extended by their political party retreats. He released a list of eight Trump cabinet nominees he intended to oppose, including Representative Tom Price of Georgia, for secretary of health and human services, and Scott Pruitt, the Oklahoma attorney general, to lead the Environmental Protection Agency.

Mr. Schumer also voiced steadfast opposition to Rex W. Tillerson, the nominee for secretary of state; Betsy DeVos, chosen for secretary of education; and Senator Jeff Sessions of Alabama, nominated for attorney general. “Nothing will change that,” Mr. Schumer said.