Well, long story short, the Priest will simply omit the papal reference. The USCCB has released a document, LITURGICAL NOTES AND RESOURCE MATERIALS FOR USE UPON THE RESIGNATION OF THE POPE which among other things addresses this:--------------------------------
The Eucharistic Prayer
In accord with liturgical norms, the Eucharistic Prayer for Various Needs I is appropriately used.
Until 2:00 PM Eastern time, February 28, 2013, the formula for mentioning the name of the Pope in the Eucharistic Prayer is to be followed as usual. After that time, during the sede vacante, the formula is adjusted as follows:
Eucharistic Prayer I (The Roman Canon) Be pleased to grant her peace, to guard, unite and govern her throughout the whole world, together with N. our Bishop, and all those who, holding to the truth, hand on the catholic and apostolic faith.7
Eucharistic Prayer II Remember, Lord, your Church, spread throughout the world, and bring her to the fullness of charity, together with N. our Bishop and all the clergy.
Eucharistic Prayer III May this Sacrifice of our reconciliation, we pray, O Lord, advance the peace and salvation of all the world. Be pleased to confirm in faith and charity your pilgrim Church on earth, with N. our Bishop, the Order of Bishops, all the clergy, and the entire people you have gained for your own.
Eucharistic Prayer for Various Needs I Lord, renew your Church (which is in N.) by the light of the Gospel. Strengthen the bond of unity between the faithful and the pastors of your people, together with N. our Bishop, and the whole Order of Bishops, that in a world torn by strife your people may shine forth as a prophetic sign of unity and concord
Thanks to Sr. Dorothy Eggering, SSND from the Office of Worship, Diocese of Dallas