Manditory disclaimer: Shimano rates their road rear derailleurs (except for the very latest models) as accepting a maximum rear cog of 27T. However (yes operator, I know), ALMOST ALL riders report these derailleurs will work fine with 30T or even 32T large cogs so you should be ok with the 28.

As badamsjr noted, your particular rear derailleur, if it's the short cage version, may not wrap up enough chain to handle to total number of teeth. So, if your chain is long enough to allow big-big (as it must be for safety) you may either need a long cage rear derailleur or be sure to not use the small chainring with a few of the smaller cogs. And, yes, if you make the cassette change, do use a new chain and be sure to size it long enough.