As demonstrations popped up across the country, thousands of calls and messages flooded the Capitol, many of them urging senators to vote against Ms. DeVos and Mr. Trump’s other nominees.

In a move that put Ms. DeVos’s nomination in question, two Republican senators — Susan Collins of Maine and Lisa Murkowski of Alaska — announced last week that they would not vote to confirm her, citing the concerns of their constituents. “I have serious concerns about a nominee to be secretary of education who has been so involved in one side of the equation, so immersed in the push for vouchers, that she may be unaware of what actually is successful within the public schools, and also what is broken and how to fix them,” Ms. Murkowski said on the Senate floor.