I hadn't heard the phrase until this year, now I've heard it a few times. Some preachers are uncomfortable 'offering Christ' in an evangelistic setting. They are uncertain whether Christ and His atonement holds true for their hearers. So instead of offering Christ (and going beyond what they feel God may be offering), they "offer the offer." That is, they tell their hearers that there is an offer of new life in Jesus. They are not so bold as to say that Jesus is "for you." But instead they are thinking that Jesus is "for some" and there's a potential that Jesus is "for you." And if an unbeliever truly repents and believes (and perseveres to the end) then that offer will prove to be for them after all.
I'm imagining that such an evangelist is uncomfortable with saying: "Christ is for you, He's truly offered to you, now through God's word, as surely as He was offered then, on the cross to the world. He is given to you as your sacrificial lamb, His blood is your atonement, have Him."
I'm imagining they wouldn't say that kind of thing, but I haven't heard enough practical examples to know how exactly they phrase things. It's quite possible that they end up saying things very similar to that.
My point here isn't about the words used so much as the theology behind it. And my one reservation is this: offering the offer doesn't sound Calvinistic enough. I know, I know - you were thinking that 'offering the offer' was straight out of 5 point Calvinism. Well the irony is, I reckon to 'offer the offer' fails to appreciate the Total Depravity that heads the 5 points of TULIP.
I'll put it this way:
If we offer Christ, we are treating unbelievers as those who are dead but here is the Resurrection and the Life for you.
If we offer the offer, we are treating unbelievers as decision making individuals who need to exercise their choice for Christ.
See the difference? Maybe it's a slight one. Maybe it doesn't matter. Maybe it doesn't lead to any real difference in evangelistic practice. But to my mind, offering the offer treats people as Hercules at the cross-roads. Offering Christ treats them as Lazarus in the tomb. I reckon Calvinists (and all who believe in the helplessness of humanity to save itself) ought to favour the latter.
If we've truly understood the plight of the unbeliever we can't offer them anything less than Jesus Himself.