How many wins over top-20 players does one need before beating a top-10 player? The answer is none. It helps one's confidence to move up the ranks gradually, but they can just as well wake up one day and beat a top-10 player without ever having done anything close to it.
The same is true here. There is no recommended number of papers to be admitted into any PhD program in the country, but it certainly helps to have a publication (or three). That said, two papers about mating habits of spotted salamanders will probably count less than a strong peer recommendation and a background in a field that is more relevant to a particular PhD program. You will hear people mention
a good fit to the program, and that's definitely one of important considerations. It may sound mythical or hazy, but the truth is that evaluators try to admit students who stand a good chance of a productive scientific career given their background and the available projects. One year we had an absolutely stellar candidate who was absolutely set on a single lab, and that lab did not have anything available. Most academic institutions don't operate like Wall Street and simply go for the best available candidates, as there is no point for them or us in getting a student who will be unhappy in the program.
When reviewing PhD applications, I try to figure out whether the candidate's co-authorship on a paper is substantial or incidental. That is usually clear from the personal statement and letters of recommendation, and I would value more one substantial contribution than two that are incidental. But publications are only a part of the whole story. In addition to the fit I described above, letters of recommendation play a major role, especially if the evaluators know the letter writers personally. It helps if the personal statement is tailored to our departmental research and faculty interests, and that usually takes couple of weeks of going through faculty pages and maybe reading couple of key publications.
My larger point is that most people can't will themselves into publishing a prescribed number of papers, even if such a requirement existed. The best you can do is: 1) make sure that your referees will write not only positive but strong letters - there is such a thing as being damned by a faint praise; 2) do your work in the lab with passion, as that will come through both in your personal statement and in recommendations; 3) carefully research the program of interest and write your personal statement in a way where they can match you with more than one lab.
My final advice is to apply to many programs that are a good match for your scientific interests. One can do good science in many places, and the prestige of Harvard and MIT means only a slightly higher initial baseline than in other places. When all is said and done, in my experience a quality student will succeed in most PhD programs.