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 health-care law: expanding health insurance coverage.