Half of all respondents said it was a bad idea for the new president to hire a close relative to serve in the government. Trump has appointed his son-in-law, Jared Kushner, as a senior White House aide, and the Justice Department has said the move is lawful.
Former Rep. Neal Smith, the Iowa Democrat who wrote a 1967 anti-nepotism law, said putting family members in office, particularly in Cabinet slots, "would be bad government, so you can't make exceptions for it."
The anti-nepotism law states that a public official may not "appoint, employ, promote, advance or advocate for appointment, employment, promotion, or advancement, in or to a civilian position in the agency in which he is serving or over which he exercises jurisdiction or control any individual who is a relative of a public official."
"Bobby Kennedy should never have been attorney general," Smith said of former President John F. Kennedy's brother, who served in his administration before the anti-nepotism legislation was enacted.
Donnelly said he was surprised at the public concern about family appointments in the Trump administration.
Just 29 percent said hiring a close relative should be legal for the president, while 44 percent said it should be illegal. Another 27 percent said they weren't sure.
"When you get below 30 percent support, you have a serious erosion of your base," Donnelly said. "He's lost the benefit of the doubt of so many Americans."
When asked specifically whether it would be appropriate for Trump to appoint his son-in-law to a White House post, 38 percent said it was appropriate, while 36 percent said it was inappropriate and 27 percent weren't sure.
Americans are also split on whether the president has come up with an effective plan to step away from management of the Trump Organization, while putting his adult sons and another executive in charge. Trump will still maintain ownership of his enterprise. Thirty-nine percent said it was not an effective way for Trump to prevent conflicts of interest, while 37 percent said it was effective and 24 percent said they weren't sure.
Trump's potential for conflicts is not the only concern for the public.
Thirty-one percent of respondents said they were "very concerned" about potential conflicts of interests with the Cabinet nominees, which include billionaires Betsy DeVos, Trump's choice to lead the Education Department, and Wilbur Ross, the Commerce secretary-designee. Another 19 percent said they were somewhat concerned, while 38 percent said they were not very concerned or not concerned at all about potential conflicts with the incoming Cabinet. Twelve percent weren't sure.
Senators held a confirmation hearing for DeVos on Jan. 17, before the Office of Government Ethics had finalized arrangements to avoid potential conflicts related to her financial holdings. Nearly half of all respondents — 48 percent — said they were very concerned or somewhat concerned that Trump's Cabinet picks may not receive a full vetting from the ethics office prior to Senate confirmation. Another 33 percent reported that they were not very concerned or not at all concerned about that issue, while 19 percent weren't sure.
Most respondents said they wanted federal background checks on nominees completed prior to Senate confirmation votes, with 43 percent saying the chamber should not even hold confirmation hearings until such checks are complete. Three in 10 adults said confirmation hearings were OK but no votes should be held until the checks are finished.
Another 10 percent of respondents said senators should hold confirmation hearings and votes right away, no matter the status of an appointee's background checks, and 17 percent weren't sure.
The Economist/YouGov poll surveyed 1,447 respondents via web-based interviews and had a margin of error of plus or minus 3 percentage points.