The number falls far below the seven that Trump's transition had hoped for, which would match the number that President Barack Obama got approved on his first Inauguration Day.
Retired Gens. James Mattis and John Kelly, nominated to run the Department of Defense and Department of Homeland Security, respectively, will likely be confirmed on Friday, Schumer told reporters.
He said Democrats would also begin debate on the nominee to run the CIA, Kansas Rep. Mike Pompeo, and he could be confirmed Friday or Monday depending on how long that process took. Schumer said some members of his caucus had "serious, serious statements they want to make about Pompeo" before voting on him.
The New York Democrat also left open the door to some unnamed "noncontroversial" nominees getting approved Friday or Monday, but declined to say who he meant.
While Republicans have a majority in the Senate and could confirm all of its nominees without Democratic support, Democrats can drag the process out for weeks if they are unhappy by requiring all procedural steps for each nominee.
Throughout the news conference on Thursday, Schumer insisted Democrats weren't being obstructionist or playing politics, as accused by incoming White House press secretary Sean Spicer earlier in the day. Schumer claimed several Republican nominees had "dramatic" ethical issues that needed to be fully vetted.
"Very easy for the President-elect to solve it," Schumer said of the delay. "Tell everyone of his nominees to submit papers and give everyone ample time, a day or two, to question them"
At the event, Schumer displayed two posters with the Democrats attack of "Swamp Cabinet" that laid out the top nominees of concern for the left: Office of Management and Budget nominee Rep. Mick Mulvaney; secretary of state nominee Rex Tillerson; Environmental Protection Agency pick Scott Pruitt; health and human services nominee Rep. Tom Price; education pick Betsy DeVos; attorney general nominee Sen. Jeff Sessions; treasury choice Steve Mnuchin; and labor nominee Andrew Puzder.
Republican senator: Mick Mulvaney could face 'problems'
Two of those nominees are already facing scrutiny from some Republicans, as well. The GOP can only lose two caucus votes before they will need Democrats to help confirm nominees.
Sen. Chuck Grassley, a top Republican on the Senate Budget Committee, warned Thursday that Trump's choice for budget director could face "problems" getting confirmed to the post because of his failure to pay taxes on a household employee.
Mulvaney acknowledged to the committee that he did not pay taxes on a household employee for four years. He later paid back taxes when learning of the discrepancy, he said in a questionnaire that was submitted ahead of his confirmation hearing next week.
Democrats seized on the news, saying such issues have forced candidates to withdraw from consideration in the past.
Now it's not just Democrats -- Grassley a veteran Iowa Republican who sits on the panel, says similar tax flaps have caused problems for other Cabinet nominees in the past and could present fresh challenges for Mulvaney.
"It could create problems," Grassley told CNN. "I don't know for sure, but I've had problems with former Cabinet people under both Republicans and Democrats where that's either been straightened out -- or if there wasn't justification for it oppose it."
Grassley stopped short of saying whether Mulvaney should withdraw.
A copy of the questionnaire obtained by CNN confirmed that Mulvaney informed the Senate Budget Committee that he repayed more than $15,000 in federal taxes on a "household employee."
A source from Trump's transition team said Mulvaney had a "sitter" for his then-newborn triplets and was unaware he had to pay taxes on her income.
Schumer on Thursday said the issue should disqualify Mulvaney -- citing the past example of President Barack Obama's Health and Human Services nominee of Tom Daschle, who withdrew for a similar issue.
"Congressman Mulvaney failed to pay taxes on a household worker, the exact same issue that caused past nominees to withdraw," Schumer said, saying it was different than other confirmed nominees who had financial issues they may have not known about. Mulvaney says he was unaware of the error.
The transition team defended Mulvaney, saying he was forthcoming.
"The fact of the matter is that nobody is more qualified and more prepared to fight to rein in Washington spending and fight for taxpayers than Mick Mulvaney," transition spokesman John Czwartacki said in a statement. "Congressman Mulvaney raised the issue surrounding the care of his premature triplets immediately upon being tapped for this position, and has taken the appropriate follow-up measures."
Schumer also targeted Tillerson, an Exxon Mobil CEO who has yet to win the support of Republicans and Russia hawks Sens. Marco Rubio, of Florida, and John McCain, of Arizona.
But Schumer said Tillerson had "huge problems" beyond his past friendship with Russian President Vladimir Putin, citing Tillerson not pledging to recuse himself from any matter involving Exxon for the full duration of his tenure.
"Oh no, there are serious problems with Rex Tillerson," Schumer said. "There'd be problems with having an oil magnate in general, but one who has been so unwilling to understand that his previous job and his future job will have conflicts of interest and he should try to be cleaner than Caesar's wife, he needs serious examination"