Opinion polls suggest Mr Menem, of the Justicialista (Peronist) Party, will score around the 45 per cent needed for an outright first round win. Even if he falls short of that, he is likely to meet the other criterion needed to avert a run-off - a score of 40 per cent combined with a 10- point margin over the nearest contender.
The incumbent's fast-sliding popularity, however, coupled with the equally rapid rise of Mr Bordon and the fact that 10 per cent of eligible voters remained undecided yesterday, left the word ballottage (run-off) on everyone's lips.
When Mr Menem last year pushed through the constitutional change that allows him to run for a second successive term - though shortened from six years to four - he was seen even by his opponents as a shoo-in. Hence his agreement to the novel run-off clause.
That, however, was before the two developments that shook Argentines out of political and economic stability. First came Mexico's devaluation and financial dbcle in December, bringing in its wake financial panic throughout South America. Since then, Argentines have moved an estimated £4.5bn out of the country, fearing Mr Menem would be forced to abandon the peso-dollar parity that has been credited with much of the recent economic stability.
Then, in March, a former navy captain broke the military code of silence and admitted helping to toss drugged detainees alive into the Atlantic from aircraft during the military regimes of 1976-83. The method was approved, perhaps even suggested, by Catholic Church leaders, according to Captain Adolfo Scilingo.
His confessions led to a national soul-searching, with army, navy and air force officers admitting collective guilt, while church leaders said they would respond later. The fact that Mr Menem had pardoned all officers convicted of "dirty war" crimes turned the issue from a moral to a political bombshell.
As Mr Menem, Mr Bordon and 12 other presidential candidates wound up campaigning last night, the President had largely succeeded in reinstating the economy as the key electoral issue. As he ended his campaign in the crucial Buenos Aires province, he and his advisers continued to push the line "better the evil you know than the good you don't know".
Mr Bordon said such comments were part of a "strategy of fear" employed by the Peronists. Mr Bordon, who left the Peronists last year to head a loose coalition known as Frepaso (Front for the Solidarity of the Country), was referring to comments by Mr Menem and his Finance Minister, Domingo Cavallo, describing Mr Bordon as a "traitor" and predicting economic chaos if he wins.
Such comments, coupled with the possibility that Mr Bordon could force a run-off, sent the Argentine stock market plunging at the start of this week. But polls suggesting an outright Menem victory, as well as an assurance by Mr Bordon to foreign bank representatives that he would maintain the peso-dollar parity, caused stocks to recuperate.
Mr Bordon was careful not to blame the Peronists for a fire which badly damaged Frepaso's Buenos Aires headquarters early on Wednesday, even though Interior Ministry investigators confirmed it had been started deliberately. Nor did he blame them directly for subsequent vandalism at a Frepaso leader's office or an attack by chain-wielding thugs on Frepaso militants putting up election posters in the capital on Wednesday.
In a matter of months, Mr Bordon, tipped to score around 32 per cent of votes, has shot ahead of the other leading candidate, Horacio Massaccesi of the Radical Civic Union. Polls give Mr Massaccesi 17 per cent of the vote.