WASHINGTON — A Supreme Court ruling this month that could overturn the ban on federal benefits for same-sex couples is presenting the Obama administration with a series of complicated and politically sensitive decisions: how aggressively to overhaul references to marriage throughout the many volumes that lay out the laws of the United States.

The decisions could affect Social Security checks, immigration laws and military benefits for same-sex couples, among other issues, with the outcomes based on whether the couples live in a state that allows them to marry.

Gay rights advocates, aware that a Supreme Court ruling that overturns the 1996 Defense of Marriage Act would be the beginning of their push to have the federal government recognize same-sex marriage, are urging White House officials to plan to modify hundreds of mentions of marriage throughout federal statutes and regulations. Many legal analysts say there is a substantial chance that the Supreme Court will strike down the 1996 law, which in defining marriage as a union between a man and a woman denies federal benefits to same-sex couples.

“We’re going to fight to ensure that legally married gay couples have access to all federal benefits and protections, irrespective of state borders,” said Fred Sainz, a spokesman for the Human Rights Campaign, a gay rights organization in Washington. “When it comes to federal benefits, it shouldn’t matter what side of a state border you live on.”