Mr Bush - whether from conviction or calculation - crossed over to the anti-abortion cause in the early 1980s. The move consolidated his position with the Republican right, but set him squarely against both a vociferous minority inside his party and a majority in the country at large.
Today, as he faces an unpredictable three-way contest for the White House played out in the heat of the country's divisions over abortion, that dilemma is deeper than ever. Paradoxically, his only consolation is that the nine Supreme Court justices failed on Monday to do what his administration's lawyers have publicly demanded - overturn the benchmark Roe v Wade ruling of 1973, that a woman's choice whether to end a pregnancy is protected by the US constitution.
Had they done so, the President's agony would have been complete. The preservation of Roe v Wade gives him at least a chance of playing down the ruling's impact, and avoiding an onslaught from his opponents that might have upset his re-election campaign irretrievably.
However, he still faces a rough ride, above all from Democrats who sense a precious opportunity to build on an apparent shift in public favour towards their derided nominee-presumptive, Bill Clinton. After weeks of drift, a combination of hard work and good fortune has begun to reinvigorate the Clinton campaign.
A Washington Post/ABC poll yesterday showed Mr Clinton, for the first time, ahead of both his rivals, albeit by the statistically insignificant margin of 33 per cent to 31 per cent for Mr Perot and 28 per cent for Mr Bush - an unprecedented low mark for the President. In the past three weeks Mr Clinton has climbed seven points, which almost certainly indicates a return to the fold of Democrats who had defected to Mr Perot. The sharpening argument over abortion offers Mr Clinton, an unbashed supporter of women's rights, fresh opportunity.
He promised yesterday that his vice-presidential running mate would be pro-choice and that a commitment to keeping abortion legal would be a 'litmus test' in his choice of future Supreme Court justices if he is elected in November. The question is far from academic. Justice Harry Blackmun, author of the Roe v Wade ruling 19 years ago, is 83 and has not concealed that his Supreme Court days are numbered.
But Mr Bush's problems are far more immediate. Despite strenuous peacemaking efforts by his strategists, and much talk of the Republican Party as a 'broad church', next month could bring a bitter platform fight on abortion at its Houston Convention.
Congressional Democratic leaders meanwhile are moving ahead with longstanding plans for a Freedom of Choice Act, enshrining in federal law the abortion rights at which the Supreme Court has been chipping away for more than three years. If a threatened Republican filibuster can be overcome, the bill could be approved before Houston. Mr Bush would have little option but to veto it, further poisoning his dispute with pro-abortion Republicans at the Convention, as well as the atmosphere in the country at large.
Some Republicans, it is true, do not see matters in so gloomy a light. In a three-way race, they argue, the President could actually benefit from a rigorous pro-life stance, if supporters of abortion split their votes between his two opponents.
Mr Perot is less outspoken on the subject than Governor Clinton. But after the Supreme Court ruling, he too is 'basically' in favour of Roe v Wade - 'My position has been and remains that this difficult decision should be a woman's choice,' he said.