The lack of nominees for the key positions comes as Trump still needs to fill nearly 2,000 appointed positions in governments -- and as Democrats continue to slow-walk confirmations of the nominees he has named.
The White House strongly disputes that it is behind, pointing the finger at Democrats for delaying the process.
Four deputy secretary positions are seen as especially important because of the role of the agencies involved in national security and the economy: deputy secretary of state, treasury, defense and deputy attorney general.
Trump has only named one nominee of those four, for the post of deputy attorney general: Rod Rosenstein, who had his Senate hearing this week.
The President also asked Deputy Defense Secretary Robert Work to stay on three months from the Obama administration but has not indicated what the long-term plan is for that position.
Trump's pace of deputy appointments lags behind his predecessors, according to data from the Partnership for Public Service, a nonpartisan nonprofit dedicated to good governance. It is also only a minute fraction of the more than 1,000 Senate-confirmed positions a President must fill.
Max Stier, president of PPS, likens deputy secretaries to chief operating officers at each agency, saying little effective management can be done without them. And, he notes, most agencies of government are currently operating amid strong uncertainty, with temporary career staffers holding these positions.
"Uncertainty is the bane of good management. And there's an awful lot of uncertainty right now," Stier said.
"An acting person is a bit like the substitute teacher. They may be a wonderful teacher, but the fact that they're the substitute teacher means they get no respect, they have no perceived authority to solve things, they don't set the lesson plan, and you also don't build the same kind of rapport with your peers across government, which is also super important," Stier added.
Nominees not confirmed
Trump himself has complained that Senate Democrats are taking too long to confirm his picks.
"I still have people out there waiting to be approved and everyone knows they're gonna be approved," Trump told the Conservative Political Action Conference last month. "It's just a delay, delay, delay, it's really sad. We still don't have our Cabinet. ... I hate having a Cabinet meeting and I see all these empty seats."
That was the White House position as well, with spokeswoman Lindsay Walters saying the lack of confirmed secretaries is part of the problem.
"If the Democrats had chosen to do their job and not slow roll the process and confirm these individuals the first day, we would have been in a different position today," Walters said. "In order to put in place a deputy you need to have a secretary. And due to the Democrats' decision to drag their feet, our pace has been significantly slowed down due to their shenanigans."
Trump has named a handful of deputies at agencies, though none have yet been confirmed. Some of the vacancies, like State and Treasury, were agencies with early secretary nominations.
By Inauguration Day he had chosen Rosenstein; his deputy at the Commerce Department, businessman and wealthy Republican donor Todd Ricketts; and an administrator for the Centers for Medicare and Medicaid Services in the Department of Health and Human Services, Seema Verma. He also before the end of January nominated Elaine Duke for deputy secretary for the Department of Homeland Security. This week, he named Jeffrey Rosen as his pick for deputy transportation secretary.
All told, Trump has named 20 non-Cabinet-level positions, including two who withdrew -- a list that includes nominees for ambassadorships, counsel positions and commissions, according to a tracker
from PPS maintained with The Washington Post. That's on top of 23 Cabinet-level nominations, including one who withdrew.
In contrast, former President Barack Obama had his deputy secretaries for state and defense named on Inauguration Day, and his deputy attorney general was named six days later. All three were confirmed by March 12 of that year. His Treasury nominee wasn't named until April, and confirmed in May.
Former President George W. Bush, who had a shortened presidential transition due to the delay in certifying the 2000 election, named his deputy defense secretary in mid-February, his deputy secretaries of state and treasury on March 8 and his deputy attorney general on March 22. Confirmation for the latter two took months.
Former President Bill Clinton named his deputy secretaries of state and treasury named on Inauguration Day and his deputy at the Department of Defense on Feb. 24. He did not name a deputy attorney general until May. All were confirmed shortly after being named.
By March 10, Obama had named 53 Cabinet-level and other positions, including nearly 10 deputy secretaries and another 10 assistant, associate or undersecretaries.
Trump has more than 1,900 vacancies within his new administration, most of which did not require Senate confirmation, according to data from tracking service Leadership Directories reviewed by CNN. The data did not include federal judgeships.
Republicans have enough seats in the Senate, a slim 52-vote majority, to confirm all of Trump's nominees after a rule change in a previous Congress that removed the 60-vote threshold for nominees.
But Democrats have used whatever tactics they can to slow down the pace of nominees -- they say to properly vet them -- including requiring lawmakers to use all the procedurally mandated time on almost every nomination and even in some cases not showing up to committee votes to deny a quorum.
The Democrats say the slow pace has more to do with Trump and his nominees than with dragging their feet. They argue Trump's nominees have not been properly vetted or present conflicts of interest that must be heard.
Trump's selections do include a number of millionaires and billionaires with complicated financial situations that have been slow to sort out. Sources close to Ricketts say he is still committed to serving, but acknowledge that his financial paperwork with the Office of Government Ethics is taking time and could be difficult to wrap up.
Other factors are seen as at play -- including difficulty recruiting. Trump may be having difficulty filling slots because some Republicans are reluctant to serve and others are being passed over because they were critical of Trump during the campaign.
Elliott Abrams, a veteran of the Reagan and George W. Bush administrations, was nixed by Trump for the No. 2 job at the State Department after he found out about criticism Abrams made of Trump during the campaign. Until then, he had been a leading contender for the still unfilled position.
There have also been reports of clashes between the White House and Cabinet secretaries of their picks, some of which Stier has heard firsthand.
"The agency hiring process is a collaborative effort between the departments and the White House," Walters said in response.
But Stier said the White House needs to recognize that it cannot select the entire government with the same process it used for the Cabinet, and needs to allow Cabinet secretaries authority.
"As with any large organization, no one individual is going to be able to run the whole place by themselves, it's going to be the team. And you need to have people in leadership that work well together," Stier said. "So while the White House has equities on who gets the job, at the end of the day, the secretaries ought to have the final say on who will be there because they are the ones who will make it work."