The meat of Piper's response comes when he says:
When I weigh the kind of imperfection involved in tolerating an invalid baptism because some of our members are deeply persuaded that it is biblically valid, over against the kind of imperfection involved in saying to a son or daughter of the living God, “You are excluded from the local church,” my biblical sense is that the latter is more unthinkable than the former. The local church is a visible expression of the invisible, universal, body of Christ. To exclude from it is virtually the same as excommunication. And no serious church takes excommunication as an invitation to attend the church down the street.You can find Grudem's response to Piper's here. It was both humorous and humble when Grudem said that his own wife found Piper's argument more persuasive. For a more comprehensive and detailed report of Piper's own understanding on this issue you can research these resources.
Since this foray, others have weighed in on the discussion. Over at 9 Marks Blog, you can find two entries by Mark Dever here and here. You can also find two good posts regarding this issue from a historical perspective written by Aaron Menikoff (Part 1 & Part 2).
In Menikoff's articles he references John Bunyan, author of of the famed Pilgrim's Progress, who made significant arguments why paedo-baptists should not be barred from the membership or communion of a local baptist church titled, Differences in Water Baptism No Bar to Communion (1673).
Sam Storms has weighed in with an article asking how these men (Piper, Dever, Mohler, Duncan) can really be Together for the Gospel if Dever and Mohler would not permit Duncan to receive communion at their church (because they do not believe infant baptism constitutes a real baptism and one must receive believer's baptism before one receives communion). Meanwhile, Ligon Duncan has stated that his response will be forthcoming.
My own view is fairly traditional within modern baptist circles. The church I pastor requires baptism by immersion after the evidence of genuine faith in Jesus Christ in order to become a member of the church and to participate in communion. However, we do not police the elements in such a way that a visiting Presbyterian could not participate although I would make it clear from the beginning before the elements are passed out what our church's view is.
Like Grudem's wife though, I find Piper and Bunyan's arguments to be weighty and biblical. I also find it contradictory to prohibit a Presbyterian from communion at the church I pastor, but would allow him to preach at the church I pastor, which I have done. This past summer I invited both a Presbyterian and Methodist to preach while I was out of town.
My hope is that this current debate will spark much fruit from future and current Ph.D students who will try to tackle these issues afresh in our day. Until then, I will be examining the more thorough writings that have been offered by Christians past.
Update: Ligon Duncan has begun his post series on why he, Piper, Mohler, and Dever can be Together for the Gospel but not together on various other doctrines.