University presidents shooting for top-tier status for their institutions pressed lawmakers Thursday to preserve funding for an initiative to help them get there, despite warnings of tough budget times, competing priorities and a tight job market. A pot of state matching funds to help the seven emerging research universities - including the University of Houston - has already been trimmed in a round of budget cuts, from $50 million this two-year period to $47.5 million, said Texas Commissioner of Higher Education Raymund Paredes.