His remarks on abortion, in particular, made during a television interview with NBC in the Oval Office, risk further exacerbating tensions with his party over its commitment, confirmed amid controversy at policy hearings in Houston this week, to outlaw abortions as a matter of constitutional law.
Asked what he would do if his granddaughter as an adult told him she was going to have an abortion, the President said he would support her in her decision. 'Of course, I'd stand by my child,' he replied. 'I'd love her and help, lift her up and wipe her tears away and we'd get back in the game.'
He responded similarly when asked how he would react to any of his grandchildren declaring they were homosexual. 'I would put my arm around him and I would hope he wouldn't go out and try to convince people that this was the normal lifestyle,' he answered.
The interview almost came to an abrupt and early end when the reporter followed up a newspaper report that Mr Bush had had an affair with a former White House aide in 1984.
Earlier in the day, the President had already denounced the allegations as an 'outrage' and 'a lie'. Seeing that the question about the alleged affair was coming again, he warned: 'Be careful now, because this interview might end.'
Looking simultaneously pained and angry, the President retorted: 'I'm not going to take any sleaze questions. You're perpetuating the sleaze by even asking the question, to say nothing of asking it in the Oval Office.' The allegations got only cursory treatment in most of yesterday's broadsheet dailies.
A small but vocal faction of Republicans in favour of a woman's right to choose abortion failed this week to force a change in the party platform's anti-abortion stand at the policy hearings in Houston. They seized on Mr Bush's television comments as proof that even he is not in line with the party position. Until 1980, Mr Bush was on the record as being pro-choice.
Most tellingly, Mr Bush, when pushed to answer whether he accepted that in the end the choice would be his granddaughter's, responded: 'Well, whose else's - who else's - could it be?'
Jane Danowitz, a member of the Women's Campaign Fund, responded: 'It is hypocrisy to continually veto legislation that allows a woman's right to choose but to be in favour of it in your own personal life, your child's right to choose.'