It doesn't make sense to me if you can hit twice as hard when spring attacking than you can when attacking without springing. So I don't think the original suggestion makes too much sense.
Then I think comrade raoul's suggestion (Lightning Strike; two attacks instead of one, the second penalized by the usual -5) makes much more sense. I think this is neat because it simply allows the fighter to get his two first normal attacks, and therefore resembles a 'normal' mechanic.
Alternatively, it could be altered a bit to resemble Rapid Shot (Rapid Strike: Req. BAB +11 and Whirlwind; make two attacks instead of one, both at highest attack bonus -2) with the obvious extension to Lightning Strike (req. BAB +16 and Rapid Strike; make three attacks instead of one, all at highest attack bonus -5). I have no idea if this is balanced, but my Rapid Strike should be equivalent to comrade raoul's Lightning Strike (-2/-2 is about as good as -0/-5). Lightning Strike is hopefully more powerful.
Rapid Strike [General]
You can deliver a pair of quick attacks in the time it would take most combatants to strike once.
Prerequisite: Weapon Focus, Dex 13+, Dodge, Mobility, Spring Attack, Int 13+, Expertise, Whirlwind Attack, base attack bonus +11 or higher
Benefit: As a standard action, you may perform a rapid strike with any weapon you have Weapon Focus with. Treat this as a normal attack action, but you may attack twice (both attacks use your highest attack modifer with a -2 penlaty). You may use this feat in conjunction with Spring Attack in order to move, attack twice, and move again (provided that you are not wearing heavy armor).
Lightning Strike [General]
You can deliver three quick attacks in the time it would take most combatants to strike once.
Prerequisite: Weapon Focus, Dex 13+, Dodge, Mobility, Spring Attack, Int 13+, Expertise, Whirlwind Attack, Rapid Strike, base attack bonus +16 or higher
Benefit: As a standard action, you may perform a lightning strike with any weapon you have Weapon Focus with. Treat this as a normal attack action, but you may attack three times (all attacks use your highest attack modifer with a -5 penlaty). You may use this feat in conjunction with Spring Attack in order to move, attack three times, and move again (provided that you are not wearing heavy armor).
Note: I changed the Weapon Focus requirement.