According to Secret Service spokesmen, a security guard spotted Mr Modjeski almost immediately after he had entered the compound and told him to stop. Mr Modjeski refused and scuffled with the guard, who either felt or saw the gun and shouted "weapon" to his colleagues. A second guard rushed to the scene and fired a single bullet which apparently hit both Mr Modjeski and the guard struggling to overpower him.
The intruder and the guard, both wounded in the arm, were said to be in a stable condition yesterday. A White House spokesman said neither the President, who was meeting his chief of staff, Leon Panetta, in the executive mansion at the time, nor Hillary Clinton nor their daughter, Chelsea, were in the slightest danger at any time.
Even so the incident - the fourth of its kind in recent months - only underlines that short of "elbow-to-elbow agents around the complex", in the words of Ron Noble, the Treasury under-secretary in charge of the Secret Service, yesterday, even the strictest security measures offer no absolute guarantee of presidential safety.
Less than four days ago, the government, without warning, closed off Pennsylvania Avenue, on the north side of the White House to traffic, to prevent a repeat of the Oklahoma City bombing. Mr Modjeski staged his intrusion from the opposite south-eastern corner of the grounds, for motives yet to be explained.
Although he had recently been dismissed from his job delivering pizzas, he had no criminal record and was not on the list of persons regularly kept under surveillance as potential assailants of the President. The pistol he was carrying was 50 years old and unloaded. "They were such a quiet couple, and I wouldn't have suspected a thing," said a neighbour in Falls Church, the Washington suburb where Mr Modjeski and his wife, Rose Mary, had lived for a decade.
Mrs Modjeski was taken from their home for questioning at dawn yesterday, as her husband remained in hospital. Law enforcement officials said he would be charged with assaulting federal officers and carrying a firearm across state lines with intent to commit a felony.
And for all his insouciance, security worries are now visibly changing Mr Clinton's habits. Lately, for example, he has been out jogging in Moscow and Kiev - but not in the early morning in central Washington, as used to be his wont. If he does jog (as he did yesterday) he goes to a military base. More frequently, though, he plays golf, slipping out for heavily guarded rounds at local courses, or practising on a new $6,000 (pounds 3,900) putting green installed on the White House lawn.
This latest intrusion is bound to produce calls for yet greater protection of the President. But short of turning the White House into a fortified military encampment, there is little more to be done. The sealing of Pennsylvania Avenue was unprecedented, but it would not have stopped Francisco Duran firing his 35 shots at the White House last October, nor the pilot of the Cessna aircraft which crashed on the south lawn a few weeks before that.
And as officials point out, the system worked on Tuesday. When he scaled the fence, Mr Modjeski tripped an alarm system and was quickly caught. Even had he not been, he would have had a hard job indeed getting close to Mr Clinton in person. Entrances to the executive mansion are tightly guarded, and the glass in its windows is bullet-proof.