Of the 1,005 people who responded to an opinion poll conducted by Reuters and Ipsos, nine in 10 Democrats and five in 10 Republicans agreed with this statement. In total, 65% agreed.
The poll suggests his illness has not widened his support, with Democrat rival Joe Biden marking his largest lead in a month in the presidential race.
The national opinion poll taken on 2-3 October suggested 51% are backing Mr Biden, while 41% said they plan to vote for Mr Trump.
Another 4% said they are choosing a third-party candidate and a further 4% are undecided.
Mr Biden's 10-point lead is one to two points higher than those he has secured over the last several weeks, although the poll has a precision limit of plus or minus five percentage points.
It appears the Democratic candidate is leading with the popular vote, but to win the presidency he must prevail in enough states to win the Electoral College.
State polls have shown that Mr Trump is nearly as popular as Mr Biden in battleground states.
The Reuters and Ipsos poll suggests 57% of Americans disapprove of the president's response to the pandemic, up about three points from a poll that ran late last week.
Only 34% believe he has been telling the truth about coronavirus, while 55% said he is not and 11% said they are unsure.
Americans also seemed to be supportive of ensuring safety during the 2020 presidential race, with 67% wanting to stop in-person campaign rallies and 59% saying the debates should be postponed until Mr Trump recovers from the virus.
The next presidential debate is scheduled for 15 October, although it is unclear whether this will go ahead.