Yet, as he must have known, it was one that has been on everyone's minds and lips here since the long-stalled Syrian-Israeli peace track suddenly burst back into life in Washington last week, when Barak held two days of talks with Syrian Foreign Minister Farouk al-Sharaa.
During the interview, Barak replied confidently that he would bring back from the negotiations with Syria "the kind of good, solid, advantageous agreement that will win a sweeping majority" in a referendum.
That, said the premier, was the only kind of agreement he would be prepared to sign.
On Sunday, Barak told his Cabinet that in early rounds of negotiations he would seek a core agreement with Damascus that covers the main issues facing the two sides. He also expressed his determination to pursue the Syrian and Palestinian negotiations simultaneously.
Despite his show of optimism during the television interview, there are many in the pro-peace camp who are concerned over the prospect of the looming referendum -- the first ever in Israel's history.
Barak's supporters all recognize that the vote will in fact be tantamount to a mid-term election -- and if Barak fails, he will have to resign.
Some in the premier's camp feel, though few are prepared to say so publicly, that he will need a substantial margin to achieve a credible win in the referendum -- something like the 56-44 percent edge by which he defeated Benjamin Netanyahu in the election last May.
This way he would not be prone to accusations from the right that his victory would be based on the votes of Israeli Arabs, while losing among the Jewish vote.
Though his supporters are buoyed and comforted by Barak's own air of confidence, many cannot shake off their anxiety as they survey the opinion polls and the perilous state of the governing coalition.
The polls show the country divided fairly evenly on the issue of withdrawal from all of the Golan Heights in return for a full peace with Syria.
If anything, the anti-withdrawal camp seems to have the edge at this time.
Meanwhile, the National Religious Party has given notice that it will secede from the coalition the moment a land-for-peace accord is signed.
The assertion has come not only from the hard-line party leader, Housing Minister Yitzhak Levy, but even from a relative moderate like legislator Zevulun Orlev.
"The minute it's signed," Orlev said Sunday, "we quit.''
Barak has courted the NRP believing that its presence within his government gives him invaluable moral and political backing in the ongoing negotiations with the Palestinians.
The fact that the pro-settler NRP was recently prepared to swallow the dismantlement of several settler outposts in the West Bank in the context of the ongoing interim accords with the Palestinian Authority was seen as an important success for Barak in his effort to represent as wide a constituency as possible in his peacemaking efforts.
The NRP may well not be alone when it secedes over the Golan.
Yisrael Ba'Aliyah, the Russian immigrant party led by Interior Minister Natan Sharansky, is likely to leave, too.
Sharansky's No. 2, Yuli Edelstein, is chairman of a pro-Golan lobby of Knesset members and is close to the West Bank settlers, too. And Sharansky himself has voiced profound misgivings over the evolving accord with Damascus.
Worse still, from Barak's viewpoint, Sharansky has gone on record with the prediction that the accord will not win a majority in the referendum. Sharansky said over the weekend he believes the Russian immigrant community, many of whom live on the Golan, will vote against it.
It they do, it would make Barak's task enormously harder.
After all, it was a significant swing within that community away from Netanyahu in the month or so before the election that gave Barak his convincing victory last May.
The conventional wisdom is that most of the Russian immigrants are hard-liners when it comes to territorial concessions.
Coming as they do from a huge country, they see no reason why tiny Israel should willingly divest itself of the geographical advantages provided by the Golan.
Nor do they have much respect for the peace promises of Moscow's former client, Syrian President Hafez Assad.
If Sharansky comes out unequivocally against the accord, that in itself would presumably affect the votes of a considerable number of the immigrants.
These uncomfortable cracks within his coalition make it all the more important for Barak to ensure the solid support of his single largest coalition partner, the fervently Orthodox Shas Party.
Shas's spiritual leader, Rabbi Ovadia Yosef, is thought to believe that the Golan is not part of the biblical land of Israel and, moreover, that land-for-peace is a worthy policy if it results in the saving of Israeli lives.
Without a doubt, Yosef has the religious and moral authority to ensure that all 17 Shas legislators vote in favor of an accord with Syria -- if he himself decides to support it.
But can he ensure the votes, in a national referendum, of the much more disparate constituency of some 400,000 people who gave Shas their votes in the May election?
Not all of these people are fervently Orthodox; some are barely traditional and voted for Shas more for its platform as the party of the poor than for its religious message.
And as the party of the poor, Shas has pretty little to show its voters for the half-year it has been in Barak's government.
With the prime minister trying this week to pass his budget bill into law before the year's end, Shas leader Eli Yishai, the minister of labor and welfare, warned Monday that the budget, poverty statistics and the Syria referendum were all intimately linked in the minds of the many ordinary Israelis who are hard pressed to make ends meet.
The minister spoke just hours after the National Insurance Institute released figures showing an ongoing increase in the number of citizens living below the poverty line.
Granted, the figures refer to the Netanyahu years; however, as Yishai and his party contend, Barak's economic policies have changed nothing in the lives of the worst-off sectors of the population. While the rich-poor gap in Israel continues to grow, the poor continue to get poorer.
Barak's reply, echoed by Finance Minister Avraham Shohat, is that returning to economic growth is a long and painful process -- one that can be dramatically accelerated by the early achievement of a comprehensive peace.
This reasoning, though theoretically impeccable, lacks cogency for many people, including many Shas supporters, who need to feel an immediate economic boost.