I've no idea whether Jenson will stay or not but I do know that Jenson has made some erratic career moves before now and that he has beaten more prestigious team mates several times. His loyalty to McLaren should be called into question when one considers that Jenson tried to leave BAR in 2004, stipulating a contract clause that allowed him to leave. The contract recognition board found in BAR's favour and Jenson was forced to stay with the team, with whom he won the championship in 2009 following the take-over by Ross Brawn.
Jenson has moved to teams with more experienced and supposedly better team-mates several times, been told he'd be comprehensively beaten several times and proved the doubters wrong several times. Here's his team-mate comparisons over the past 13 seasons with the highest scoring driver highlighted in bold:
2000 - Williams: Button 12 points - Ralf Schumacher 24 points
2001 - Benetton: Button 2 - Fisichella 8
2002 - Renault: Button 14 - Trulli 9
2003 - BAR: Button 17 - Villeneuve 6
2004 - BAR: Button 85 - Sato 34
2005 - BAR: Button 37 - Sato 1
2006 - Honda: Button 56 - Barrichello 30
2007 - Honda: Button 6 - Barrichello 0
2008 - Honda: Button 3 - Barrichello 11
2009 - Brawn: Button 95 - Barrichello 77
2010 - McLaren: Button 214 - Hamilton 240
2011 - McLaren: Button 270 - Hamilton 227
2012 - McLaren: Button 188 - Hamilton 190
In 13 seasons Jenson Button has beaten his team-mate 8 times and has been beaten 5 times. He has beaten 2 world champions in the same machinery when both times he was told beforehand that he would be annihilated.
Jenson may or may not move to Red Bull as Sebastian Vettel's team mate. But if he does the records show that he won't be the walk-over many are writing him off as.
Button's reputation seems to be similar to Damon Hill's. Both are world champions and both showed that they can beat higher rated drivers in equal machinery - despite commentators saying otherwise.