Ches has made the eminently sensible point that petitioning the Holy Father is something that Catholics do, and, traditionally, always have done in one way or another. In every hierarchical society there has to be a means whereby those at the bottom have a means of making known to the senior hierarch what they think. There are tactical problems surrounding on-line petitions: verification of the "signatures", for example, and how you measure success. But nobody can deny us the opportunity to present our case to the Pope and hope that he takes into account that a number of people feel sufficiently exercised to make him aware.
What people (though Ches was on the money once again here) seem to have missed is that the petition will be an input to a process in the same way that the leaked draft "clarification" was, and that the nature of the input varies in accordance with whether it is made in public or in private.
There is a whole host of people trying to express a view on Summorum Pontificum: people in the several Congregations which have some locus, those in Congregations that don't but which think they should, interested and disinterested (are there any uninterested?) senior Cardinals, curial officials who have access to any of the above, Nuncios reporting on what their local Episcopal Conference thinks, the Heads of National Colleges in Rome, the Rectors of Pontifical Universities: in short we are in Rome and this is how things work.
Whatever some people might want, the Pope is not omnipotent. His actions are restricted not just by the Magisterium but by both the realities of where power lies between the different dicasteries and senior clerics and by where SP fits into his overall plan. If he is to bring the largest possible number of people with him across the programme as a whole, he will have to compromise, more or less, here and there. He already knows already , for example, that the mere fact of issuing SP did not mean that his motu proprio - his own word - was immediately acted on by the Bishops of the Church.
The internal politicking - the clamour to have one's point of view heard - takes place in various different media and fora, and the leak of the draft obeys the strategy of whoever leaked it. Was it to galvanise supporters of SP? Was it to try to salvage some crumbs for the about-to-lose opponents of SP? Was it leaked by a supporter or an opponent? There is no simple answer to the question Cui Bono?
It's worth signing the petition just to be part of the process and to add slightly the the influence being exercised in one particular direction, but the petition won't radically change anything the Pope eventually signs, just as the leaked document will just have been somebody's input to the process.
Whatever document ends up appearing: whether a new motu proprio, an instruction, a clarification, it will not be checkmate for the Pope against "them", whoever "they" are: it will simply be the next move. I'm praying for the game, and for the player, rather than for the move.