Faced with severe budget problems, Republican governors are escalating their fight against federal rules requiring states to maintain current levels of health-care coverage for the poor and disabled. The growing resistance to the federal government over the hugely expensive Medicaid program poses a critical test for President Obama, who has the power to relax the rules for states. If he allows states to tighten eligibility requirements, it would outrage many of his core supporters while undermining the central goal of his signature healthcare law: expanding health insurance coverage. But if the president turns his back on governors struggling to gain control of their finances by trimming their most costly program, he risks intense criticism just as his administration is locked in a battle with Republicans over the nation's soaring debt. "There is a growing impatience among governors," said Mike Schrimpf, communications director for the Republican Governors Association. "As the Medicaid portion of state budgets grows, the issue becomes even more pressing."