I believe Button is just posturing for his fans and/or letting his pride get in the way of common sense. But I've already said that I find it unlikely that Jense would find himself in a position to help out in any meaningful fashion anyway.
One thing is clear though that both McLaren and Red Bull should be concerned about. Teammates that fight out a year long battle for supremacy rarely end up with the WDC crown, unless of course both car and driver are well ahead of the pack like the Senna/Prost McLaren days.
The prime examples of this scenario are 1986 and 2007, where two drivers from the same team often took points off each other, allowing another driver to stay in touch and eventually overhaul the two others. Unsurprisingly, these are really the only two seasons (since 78) where multiple drivers from one team were battling with a driver from another team for the title at the very end of the year.
Since 1990, the World Champion has beaten his teammate by a very comfortable margin in all but a couple seasons. Interestingly, 2007 was the smallest margin of victory by a WDC over his teammate (16 points), which I suppose illustrates the dominance of the Ferrari's and McLarens that year. Only in 1996 (19 points) and 2009 (18 points) was the winning margin of the WDC over his teammate less than 20 points, and 2009 was a very odd championship where the WDC drove the 2nd half of the season in cruise-control. So we're left with 1996 as the most recent example of where two teammates battled throughout the season and one still came out with the championship. And I think it's fair to say the competition from the other cars in the field was underwhelming that year.
Bottom Line: If you are fighting a close battle with a constructor that has their eggs firmly placed in the basket of a specific driver, you had better get behind one of your own if you want to win the WDC.