MetroHealth System executives are facing a public inquisition. As the new Cuyahoga County Council begins its first two-year budget process, there were signs late last week that the county-owned health system's top leaders will not walk away with a proposed $72 million taxpayer subsidy without some pain. The recent announcements that MetroHealth would cut 450 jobs and close a 144-bed skilled-nursing unit to shave $30 million from its annual budget have put a spotlight on lingering questions about how the health system operates. "They are going to have to adjust to the idea of not going to one county commissioner and whispering in his ear about what they're doing," said Dan Brady, chairman of the county's health, human services and aging committee, which held a public hearing on MetroHealth on Thursday.