Arriving just before her half-time Super Bowl gig on Sunday, Madonna debuted her new single and video last night on "American Idol" and is clearly hoping for a marketing touchdown this weekend.

The new song, "Give Me All Your Luvin'," features modern hip-hop/dancefloor queens M.I.A. and Nicki Minaj, who have decidedly minimal roles in the single but are featured prominently in the video as cheerleaders – vaguely in all-hail-Madonna fashion. In a promotional tie-in that seems too good to be coincidence, the clip also features a bunch of dancing football players. The lads swirl around with Madge and hold her over her head in scenes reminiscent of her classic "Material Girl" video. There are also cheering crowds, fireworks and falling confetti in the background of the clip.

Basically, it looks like she geared the whole thing around this half-time appearance, so much so that you expect to see some kind of Bud Light advertising placement in the video. The song itself is a catchy little number, as breezy and fluffy as "Lucky Star" but with a cool dance groove. It's available for download on iTunes, where it can also be bought with a pre-order for the new album, "MDNA," due out sometime in March.

Undoubtedly, we can expect to hear "Luvin'" during Sunday's half-time appearance. Both M.I.A. and Minaj are even reportedly set to join in. That's just the front line of the marketing blitz, though. Clear Channel has pledged to play ""Luvin'" on participating radio stations around the country at the top of every hour today through Sunday. Clear Channel is also reportedly dedicating 1,600 of its electronic billboards around the globe to Madge ads. Meanwhile, Clear Channel's former corporate parent, Live Nation – who represents Madonna in a so-called 360 management deal where it handles all facets of her career – is expected to announce details of her upcoming tour after the Super Bowl. It's expected to include her first Twin Cities date in over two decades.

Lost amid all this hoopla is Madonna's movie, "W.E.," about King Edward VIII's divorcee wife Wallis Simpson, which the pop star directed. The film came out in limited release today, but no Minneapolis opening date has been set. That might have something to do with its paltry 18% rating so far on RottenTomatoes.com.

Oh Madge, stick to what you do best -- hyping yourself in the pop music world.