Dennis Rivera, the president of New York?s largest health care union as well as its most politically powerful union, announced today that he would be stepping down. Mr. Rivera announced that after 17 years as president of 1199 S.E.I.U., he would become chairman of his parent union?s million-member health care division to help it grow faster and become a more potent political force, especially in the push for universal health coverage. Mr. Rivera, whose Manhattan-based union local has nearly 300,000 members, said he would not run for re-election and would step down on June 15, when his term ends, unless New York State?s budget process is completed before then.