To give a more realistic understanding of this question, consider that in the last 40 years or so of US presidential races, the number of eligible citizens who do not vote at all — many of whom don't even register — is roughly equal in size to the votes cast for each political party. In other words, the country seems to be divided in rough thirds: Those who vote Democrat, those who vote Republican, and those who do not vote at all, with a percentage who shift between groups from election cycle to election cycle. If we make the coarse assumption that all of those non-voting citizens decided not to vote because they dislike both candidates, and if we gave those citizens a 'None Of The Above' (NOTA) option, then it is perfectly realistic to think that NOTA might win the popular vote in a US presidential election. And this is in the context that presidential elections have higher turnout and higher response rates than elections for any other public office in the US. US Congresspeople, state legislators and governors, local officials, elected judges, etc often win their seats with tallies as low as 10% of their eligible constituency. If almost 80% of eligible citizens don't bother to vote for a particular office, how difficult would it be to convince (say) one-fifth of those people to vote NOTA? That would give a roughly 15% vote share to NOTA, ensuring its victory.
Now, the main argument against 'None Of The Above' options on ballots is that we need political offices filled to maintain our system of government. Things will fall apart, so the claim goes, unless there is someone at the helm guiding the ship. This is a valid point, to an extent, but it's important to note that most of the actual work of government is carried on by institutions and agencies — non-elected civil servants grinding through the daily tasks of providing government services — and these institutions and agencies are quite capable of carrying out the work of government in the absence of a politically elected leader. Political leaders are important to guide the course of government and keep these agencies and institutions in tune and on track, but the system as a whole will maintain consistency — at least for a while — just the way that a ship will continue floating if its captain decides to run off with a mermaid (or, whatever...). There are risks in allowing elected offices to remain empty until a clear public mandate is established — sudden crises or problems might crop up that call for leadership — but the system as a whole will not immediately crash and burn because there is no one occupying the leader's seat.
There are also some distinct advantages in adding a 'None Of The Above' option, at least from the perspective of the citizen. The prospect that a large NOTA vote might nullify an election is a strong incentive for political parties and candidates to run inclusive, non-divisive campaigns. Offending potential voters becomes politically dangerous; winning an office demands pulling people into one's camp, and cannot rest on alienating people in the opposing camp. It would shift more attention to underserved groups, who are most likely to vote NOTA out of a sense of frustration, and would place a check on candidates to keep them from straying too far from the interests and needs of their constituents.
However, this would be 'hair-shirt' representative democracy. Citizens would have to be willing to accept the risks that come from an absence of leadership in order to achieve the goal of more responsive and responsible leadership, and that is an uncomfortable prospect. The transition to such a system would terrify many people (who prefer the security of always having someone in charge, no matter how terrible they might be), and even after it was established and institutionalized it would involve a constant struggle of wills between the citizenry and the parties/people vying to be their representatives.