We report the most restrictive direct limits on masses of fourth-generation down-type quarks b{'}, and quarklike composite fermions (B or T{5/3}), decaying promptly to tW{-/+}. We search for a significant excess of events with two same-charge leptons (e, mu), several hadronic jets, and missing transverse energy. An analysis of data from pp collisions with an integrated luminosity of 2.7 fb{-1} collected with the CDF II detector at Fermilab yields no evidence for such a signal, setting mass limits m{b{'}}, m{B}>338 GeV/c{2} and m{T{5/3}}>365 GeV/c{2} at 95% confidence level.