Responsibility in Federal Contracting Act - Requires that the locally prevailing wage paid to various classes of laborers and mechanics working under federally-financed or federally-assisted contracts for construction, alteration, and repair of public buildings or public works (Davis-Bacon Act) be determined by the Secretary of Labor (as under current law), but acting through the Bureau of Labor Statistics (BLS), using surveys carried out by BLS that use proper random statistical sampling techniques.