This was a busy week for rumors about FaceTime — the Wi-Fi-based video conferencing protocol that Apple (AAPL) introduced on the iPhone 4 in June and added to the iPod touch two weeks ago.

The one that got the most attention was AppleInsider‘s report that the company is speeding up development of a camera-equipped iPad that could run the protocol. Less prominent was the rumor in the Paris-based blog Mac4Ever that Apple is preparing to ship a FaceTime version of iChat that could, in theory, let iPhone 4 owners make video calls to any Macintosh equipped with a camera and a microphone.

So how does all this help Steve Jobs deliver on his promise — made back in June — to ship “tens of millions” of FaceTime devices this calendar year? Let’s run the numbers:

First of all, it’s entirely possible that Jobs could do it with the iPhone 4 alone. Piper Jaffray’s Gene Munster — to pick on just one analyst — estimates that Apple will sell 11 million iPhones this quarter and 11.4 million next quarter, although some of those units are iPhone 3GS models that don’t support FaceTime.

The new iPod touch, which began shipping this week, will almost certainly put FaceTime over the top. Apple will probably ship a couple million this month, and Munster estimates that it will sell 10.5 million in the quarter that starts Sept. 26.

The iPad probably won’t help much, even if — as one dubious rumor has it — Apple manages to ship a few of the camera-ready units before the end of the year.

But if FaceTime does come to iChat before Christmas, that would allow Jobs to include in his total all the iMacs, MacBooks and MacBook Pros Apple ships in calendar 2010 — an estimated 13.4 million units, according to Munster.

Grand total: roughly 48 million FaceTime devices.

For the record, this is what the Yankee Group’s Carl Howe told Computerworld back in June:

“I think tens of millions is a stretch with the current product line. You can assume iPhone 4s will sell easily a million a month for the next six months, but that only gets you to 6 [million] to 8 million units.”

If Apple were to introduce a second-generation iPad with a front-facing camera, “that would get us [to tens of millions] perhaps, but such a fast rev of that platform would be dangerous, although not unprecedented for Apple, for early adopters.”

[Follow Philip Elmer-DeWitt on Twitter @philiped]