Whether or not you would need a different strategy is debatable, but you would almost definitely see one. Voters in less populous states are over-represented in the EC, and urban voters are a key Democratic constituency, so you would definitely see messaging shifting away from things that would appeal to farmers in Iowa, since it would cease to matter (think things like mentions of ethanol as an energy source in stump speeches), and towards things that would drive up Latino turnout in Los Angeles: heavier discussion of immigration reform, for example, which very rarely came up in this cycle -- the foreign policy debate didn't mention drug violence in Mexico at all, this time, I don't think, and instead focused entirely on the middle east.

I think lots of "urban" issues would suddenly be much more relevant to the campaign, particularly on the left; gun control would be back on the table, marijuana legalization would start to be taken seriously as a social justice issue, etc. I'm partly talking out of my ass, but things would almost definitely change.