A topic that has been discussed at length over the last few years has been the practice of lay people giving blessings to individuals during communion. It is technically not appropriate for this to occur. As a result, what to do when someone approaches an Extraordinary Minister of the Eucharist (myself included) for a blessing has caused some difficulties. In fact, it is my understanding that neither a priest or a deacon should give a blessing during communion.
However, I read an interesting discussion of this problem by Bishop Chaput of Denver. He said that the words "Receive the Lord Jesus in your Heart" can be spoken by either a Priest, Deacon or Extraordinary Minister of the Eucharist. These words are not a blessing but an invitation into this mystery. More of Bishop Chaput's explanation as well as more debate on this topic can be found HERE.