With the fate of health insurance for 30,000 legal immigrants hanging on the choices legislative leaders will make in the coming days, House Speaker Robert DeLeo said Gov. Deval Patrick made a "good and compelling case" for maintaining the coverage. He added, though, that lawmakers were still concerned about financial constraints and had yet to finalize plans for dealing with budget issues. His remarks came minutes after Patrick's top budget and human services aides emerged from the speaker's office Monday afternoon. Secretary of Administration and Finance Leslie Kirwan, who chairs the state board implementing health care reform laws, and Secretary of Health and Human Services JudyAnn Bigby walked directly from DeLeo's office into the governor's suite, with Bigby declining to answer questions from reporters. The governor told reporters Monday afternoon that paying for coverage for the immigrants was an example of tough fiscal choices policymakers are exploring. “Are we going to support health care, or are we going to support some of these other ideas?” he said. “It’s important to hospitals. It’s important to taxpayers. That is a part of the health care framework that we’ve been working on.” A spokesman for the state Connector Authority, the agency handling day-to-day implementation of the health reform laws, told the News Service officials were "doing preliminary modeling" of a special plan for the immigrants, should the Legislature go along with the governor's request to fund their health care. All 30,000 will lose coverage at the end of the month under the budget adopted by the Legislature and signed by the governor, unless lawmakers approve a plan the governor filed separately to maintain the coverage.