It is likely that Obama is still going to be focusing on gay rights issues. He's done little in the immigration policy, which was something he promised and which got him re-elected. If the Republicans were to focus on the issue, they may gain the upper hand in the next presidential election. I think this is the only card they can play. Not LGBT, not the same old craps. I would have picked Obama anytime, not because Obama was better, but because the Republicans were really that bad.
However, if both sides realize this and only care about winning, there could be chaos.