The ageing president’s oldest child is currently facing his own battles, following his federal gun conviction earlier this month and a trial set for September over tax evasion charges.
Mr Biden’s family are said to be accepting of how poorly he performed against former president Donald Trump – but have expressed frustration with the aides who prepared him for the event.
Another person privy to the discussions told The New York Times “the entire family is united”, adding that there was no talk of Mr Biden backing out.
The 81-year-old president has previously said he would never run a political campaign without the backing of his family.
Further sources said Mr Biden was upset by the criticism but was committed to staying in the race. In private conversations, he has reportedly asked his aides and allies about what they are hearing in the Democrat camp.