Public refusals by two US Senate Republicans to support Betsy DeVos for education secretary has raised the possibility of a rare congressional rejection of a Cabinet nominee.
With Democrats expected to oppose Ms DeVos' approval as a block, they would only need three Republicans to side with them to make Ms DeVos just the tenth cabinet nominee in US history to be rejected by Congress.
Mr Trump's nominations for cabinet positions require approval by a Senate committee vote then, if successful, by the full Senate.
Ms DeVos' nomination barely squeaked through a Senate committee vote on Tuesday, with Republican senators Susan Collins and Lisa Murkowski both saying they voted yes only so the entire Senate could debate the matter.
"I cannot support this nominee," Ms Murkowski said of DeVos, a billionaire philanthropist with no experience working in education who is a strong charter-school advocate, in a floor speech.
Ms Murkowski said she needed to make her intentions clear to her colleagues.
Ms DeVos' opponents kicked into high gear on Wednesday to press other Republican Senators to vote no when the chamber begins considering the nomination, expected as early as Wednesday afternoon.
Ms Collins and Ms Murkowski would be the first Republicans to break party ranks and vote against one of Mr Trump's cabinet selections.
Soon after Collins and Murkowski staked out their opposition to Ms DeVos, the White House said it was confident she would ultimately be approved.
Mr Trump's early nominations, primarily for security posts, had an easier time on Capitol Hill than names now before the Senate.
Republicans hold majorities in both the Senate and House of Representatives, but Democrats have been on a blitz to try to block the nominations, often raising concerns about conflicts of interest.
The party has to tread carefully about approving one nomination, that of Alabama Senator Jeff Sessions for Attorney General, who would have to vacate his sentate seat if successful making him unable to support Mr Trump's other nominees.
Mr Sessions' nomination as attorney general was approved in a full justice committee vote along party lines on Wednesday.
Possibly in a sign of things to come, Republicans on a US Senate committee changed the rules in order to allow Mr Trump's picks for health and treasury secretaries to go through despite a Democrat boycott.
After Democrats on the finance committee said on Tuesday they needed more time and more information about Mr Trump's selections of Tom Price for health secretary and former banker Steve Mnuchin for treasury secretary, Republicans on the finance committee got them through anyway.
They suspended a rule that requires at least one Democrat to attend the vote so they could go through despite the opposition party's absence.
On Wednesday, the Senate Finance Committee had to suspend its rules to advance Treasury Secretary nominee Steve Mnuchin and Health Secretary nominee Tom Price to the full chamber for approval, the final step in the confirmation process.
Committee Democrats on Tuesday had boycotted the vote, forcing Republicans to scrap a requirement that at least one Democrat be present for a vote.
Confirmation hearings for Labor Secretary nominee Andy Puzder have been delayed over ethics filings.
Meanwhile, the Senate confirmed Rex Tillerson as secretary of state on Wednesday, filling a key spot on the national security team despite concerns about the former Exxon Mobil chief executive's ties to Russia.
The US Senate voted to confirm Mr Tillerson with 53 votes, with 42 voted against.
The vote was largely along party lines, with every Republican supporting Mr Tillerson and nearly every Democrat opposing him.
Some faulted him for failing to promise to recuse himself from matters related to Exxon Mobil businesses for his entire term as secretary of state rather than only the one year required by law.