President Obama has directed a small team of advisers to develop a proposal that would keep the government playing a major role in the nation’s mortgage market, extending a federal loan subsidy for most home buyers, according to people familiar with the matter. The decision follows the advice of his senior economic and housing advisers, who favor maintaining the government’s role as an insurer of mortgages for most borrowers. The approach could even preserve Fannie Mae and Freddie Mac, the mortgage finance giants owned by the government, although under different names and with significant new constraints, said people knowledgeable about the discussions.