Character generation would be dead simple. Assign a maximum point value that players can spend, and let them purchase a character with that. Role play your superhero/villain. When combat breaks out, use the Clix rules to resolve it. For other tasks, role play/negotiation ("I've got super strength, of course I can lift the bus"), or a 2d6 roll against a target number set by the GM would work (TN 10 to lift the bus normally, TN 5 with super strength).
For character advancement, I could see two systems that could be easily used. Both have advantages and disadvantages, though.
First, using the Rookie/Experienced/Veteran versions of the figures. This would likely require getting some figures from the secondary market, unless someone in your group was a die hard serious Clix collector. The GM could set a certain number of XP required to advance, and award XP for goals achieved and villains defeated. Alternately, a set number of 'plot points' or simply games played might be enough to level up. [alternate models of the same character from different sets could also be worked in, judging relative strength by point cost of the figure]
Benefits: Players start and continue to play the same character through the campaign. Possibly less bookwork to keep track of as well (if a simple X games at Rookie allows promotion to Experienced).
Drawbacks: Players might not be able to play as the character of their choice (Rookie Batman is more powerful than Veteran Gambit) due to the starting point ceiling. Limited growth arc (3-steps).
Second would be a system similar to the point-keeping used in a normal game to determine a winner (points awarded for point-value of villains defeated, or team-members still standing, plus throw in some goal/plot based awards for non-combat stuff). In this system, though, it's not the characters gaining experience, it's the PLAYERS. So it would be less XP, and more Player Privilege Points (P3 for short?). Players keep a total of the points they've earned, and the points divided by 10 determine the maximum they can spend on a hero to play each session.
Benefits: Much greater growth potential, characters could start out as Shield Agents or other 'grunt' figures, then work their way up eventually to the Superman/Hulk/Thor level. Players can try out lots of different characters along the way. Hero/sidekick combos could also be allowed if the points are there for both.
Drawbacks: Long term story lines could be hard to do, as the cast of heroes would likely be changing from session to session, especially when players don't earn enough to purchase the same figure they played last session at the next higher level. More bookwork tracking P3.
Finally, GMs would need to include 'break points' or morale or something to keep fights from going to the bitter end every time. Sometimes it's fine to run those long combats until one side or the other is done, but most of the time that might take too long. Then again, if 4E people are willing to play through hour+ long combats in their D&D, some people might also in their Supers RPG.
Of course, the big downside of all of this thought experiment is that there's no way (without some plastic molding skills and equipment, anyway) to really make your own heroes. You're stuck playing ones from the HeroClix game (and apparently, only from the earlier sets if you use Advancement Method 1 above, as it looks like the more recent sets have done away with the R/E/V levels.)