According to VGCHArtz:
"Nintendo's latest console, the Wii, which was released in November 2006 in North America, and December 2006 in the rest of the world will surpass the lifetime sales of the Nintendo Gamecube by February 16, 2008. Through February 9, 2008 Wii has sold 21.490 million consoles, while Gamecube had sold 21.515** million consoles. Worldwide, Gamecube has been selling fewer than 500 units per week lately, while Wii has been selling several hundred thousand units per week. Using the week ending February 9th, when Wii sold 447,000 units in one week as an estimate rate of increase (~64,000 units sold worldwide per day) for the week ending 2/16 Wii lifetime sales caught and surpassed Gamecube lifetime sales on February 10th, 2008. Even if Nintendo only ends up selling 175,000 Wiis for the week ending 2/16/08, Wii passed Gamecube on February 10th, 2008. Considering Nintendo sold nearly 300,000 Wiis just in the Americas and Japan for the week ending February 9, 2008, it is very unlikely Wii has not already passed Gamecube lifetime sales as of the writing of this article (February 14)."
Congratulations to the Wii it only took them 1 year and 3 months to surpass the Gamecube.