I'm afraid I don't know about what the Constitutional Convention considered. I don't even know if it's possible to know since the meetings were secret. One of the Americanists will have to come along for that. I do have a point to make about Roman stuff though.

We do have an elected position with a veto - the presidency. However our kind of veto is different from the Roman sort; the pres can veto legislation; the tribunes (and other magistrates for that matter - people often forget Roman magistracies are collegiate so that one magistrate can provide a check on the other) vetoed magisterial action as well as legislation. The Latin term isn't "veto" but "intercessio"; it's literally a "coming between" the magistrate and the object of his action. So, for instance Caesar writes that Marcellus, as presiding consul, forbade the consideration of a motion that Juba get Friend and Ally status, and a tribune Phillipus vetoed a motion to appoint Sulla propraetor of Mauritania, but "de reliquis rebus senatus consulta perscribuntur" - "about the rest of this stuff decrees of the senate were written out." So unlike the Presidential veto, which is exercised after a bill passes the legislature, the Roman veto prevented even consideration of a matter.

I think. Roman law is complicated. I checked the OCD and New Pauly; both of them stress intercessio as a restraint on magistrates. I also flipped quickly through Greenridge's book on Roman legal practice and didn't find anything opposing this view, but I'm sure someone somewhere thinks vetoes work some other way.

For reference, here's part of the New Pauly entry:

In Roman Republican constitutional law, the intercessio (from intercedere = to step in-between) denoted a veto against magisterial decrees ( Decretum ), against Senate resolutions ( Senatus consultum ) and against rogations of all types presented to the various people's assemblies. It rendered decrees ineffective unless an intercessio was unlawful, as for example in the case of magisterial court decrees during an ongoing legal proceeding. Senate resolutions were reduced to mere recommendations ( auctoritas ) and rogations became void if the people had not yet decided on them. This right to veto was held a) by every officeholder with respect to a colleague of equal rank, b) by every officeholder with respect to officeholders of lower rank, c) by every officeholder with respect to Senate resolutions unless they had been co-authored by higher ranking Senate members, d) every people's tribune with respect to all officeholders (except dictators), to all Senate resolutions and all rogations presented to the people's assembly.