"Always, both by word and deed, have I protested how eager I was for unity. Mine, however, was a unity of the Church, which should begin with thee and end in thee....nor did I think that I dissented from thy Church, because I was at war with those leaders; for thou hast forewarned me, both by thy Son and by the apostles, that that place would be occupied by persons to whom I ought by no means to consent...and the apostles declared that there would be no enemies of thy Church more pestilential than those from within, who should conceal themselves under the title of pastors. Why should I have hesitated to separate myself from persons whom they forewarned me to hold as enemies? I had before my eyes the examples of thy prophets, who I saw had a similar contest with the priests and prophets of their day, though these were undoubtedly the rulers of the Church among the Israelitish people. But thy prophets are not regarded as schismatics...They still remained in the unity of the Church" (Reply to Cardinal Sadolet).
Calvin seems to believe that despite the reformation movement unity is nevertheless perserved, and hence that invisible unity (and visible dispersion) of the Church is adequate. Moreover, he thinks that such a state of affairs is preferable than the visible unity of a Church hankered with "strange doctrines" and "superstitions" (such as transubstantiation, confession and penance, revering saints and icons, papal rule, indulgences, etc.).
For awhile now, I've been hoping that invisible unity would be sufficient to preserve the kind of love and harmony that Christ and Paul had exhorted for the disciples. These days, I'm less sure of that. For what would be the (invisible) relation that holds the disciples of Christ together? The most obvious answer would be a set of beliefs and practices, perhaps the ones laid out in C.S. Lewis' Mere Christianity. However, I don't think that these "fundamentals" are either sufficient or even necessary to count one as a Christian of any denominational stripe (I'll say more on this at some point).
Another answer could be, as Calvin seems to say, Christ Himself (or in another way, God "Himself"--supposing that 'God' refers to a self). But this answer is either trivially true such that it is uninformative as how we ought to actually live out in unity, or it says too little and so again is not clear as to how we ought to actually bring unity about.
RC has an easy answer to this, which is the fellowship that is grounded in doctrine, the sacraments, and the magisterium. Regarding the first, there is no problem as the one that besets protestant unity (I'll say more on this... but this should be obvious given the recent up-in-arms from evangelical protestants [especially the reformed variety] against Rob Bell). The second is something I'll say more about later as well. As to the third, it is grounded by Christ's establishment of Peter's role, and the ecumenical bond that is preserved through apostolic succession--the membership in a lineage that begins with Christ and the apostles and moves all the way up to the present with the Roman See (of course EO can make a similar claim too). Thus, Benedict XVI is a symbol of a unity that is both synchronic (all the faithful throughout the world) and diachronic (all the faithful past and present); and this unity is clearly visible.
Another way of putting it is that RC finds unity in Christ Himself. However, unlike the protestant claim, there is much more substantive content to what that means--it has more meat for me to sink my teeth into.
I'm still somewhat hopeful for the possibility of protestants discovering a means to maintain unity (and of course, it will have to be grounded in Christ Himself). But unless we evangelical protestants can say more, I take this to be a knock against our side.
(and if anyone has reasons for believing unity [whether visible or invisible] is not required, I'd like to hear it... though I currently take it as a non-starter given Matthew 17)