I can see Martinez moving if he wants a proper shot at more than an occasional cup or cup challenge. The odds are stacked against him if he stays at Everton, assuming their budget remains the way it has been. He loses Lukaku in the off-season, and who knows if he'll be able to acquire him permanently or on loan again for another season. Who knows what Kone can do next season? He practically didn't play this season due to injuries. And that loan from Monaco - Lacina Traore - was Everton's answer to Arsenal's Kim Kallstrom.
Then there's the replacement work he needs to do at the back which I've mentioned before - Distin is 36 and will need replacing soon, while Jagielka is 31. So that's a few things he needs to be looking at, and he'll need a bit of money to do it. Put another way - if Martinez wants to win something, he probably has a better chance at a club that's demonstrated a greater willingness to spend. He'll try to build his reputation at Everton in these couple of seasons but if money isn't available and a chairman/owner with greater willingness to loosen the purse strings comes knocking, he'll be off in a hurry.
Here's the Wiki entry on him, regarding his move from Swansea to Wigan:
---------
Throughout his time at Swansea, Martínez was often linked with other managerial jobs, but he repeatedly stated that he would only leave Swansea as manager if he was "forced out." As his success grew, he publicly criticised players that left the club for money or for larger clubs. In June 2009, both Celtic and Wigan Athletic asked Swansea for permission to speak with Martínez regarding their managerial vacancies, with Wigan being granted the opportunity to hold talks with Martínez. After several days of negotiations, Martínez was confirmed as the new manager of Wigan, taking four backroom staff with hi. Martínez signed a three-year contract worth £1.5 million and was assured by Wigan Chairman Dave Whelanthat his job would be safe for the next three years, even if the club suffered relegation.
Wigan Athletic
Martínez's move to Wigan was not without controversy. Many Swansea fans were upset that he had chosen to leave the club despite his previous comments that he would have to be "forced out" to leave the club, and he was subsequently nicknamed "El Judas" by some fans. Martínez explained that his decision had been a difficult one to make, but felt the opportunity to manage in the Premier League at the club where he began his English footballing career was too good to turn down.
---------