WASHINGTON — Senate Democrats concede they have little leverage to stop Donald J. Trump’s cabinet nominees. But that will not discourage them from trying to make life as uncomfortable as possible for many of his choices, with the hope of forcing their Republican colleagues and Mr. Trump to squirm along the way.

With nominees like Representative Tom Price, a proponent of fundamental changes to Medicare, to be health secretary, and Steven Mnuchin, a Goldman Sachs trader turned hedge fund manager, as Treasury secretary, Democrats hope to use the confirmation hearings to highlight the wide river of incongruities between Mr. Trump’s campaign promises and much of the team he is assembling. The goal: to fuel a narrative that the incoming president, and the Republicans who support him, cannot be trusted.

“President-elect Trump promised that he was going to clean up the swamp,” said Senator Chuck Schumer of New York, the incoming Democratic leader, “and a whole lot of his nominees have had their career in the swamp.”

One by one, Mr. Schumer said, Democrats will use the confirmation process to highlight positions held by nominees that are either inconsistent with Mr. Trump’s campaign promises or raise the sorts of ethical questions that Democrats tried in vain to hang around Mr. Trump’s neck during the campaign, like refusing to release his tax returns. Senator Elizabeth Warren, Democrat of Massachusetts, who serves on committees that are likely to have contentious hearings, can be counted on to work over many nominees.