The exception now is a spouse, sons, daughters, parents, legal guardians, siblings, grandparents, grandchildren, aunts, uncles, nieces, and nephews. That would certainly be a positive move, but I don't think the safe third country agreement is salvageable by any expansion of the exceptions. I think it's based on a fundamentally problematic assumption that has not been investigated in five years, which is whether the United States meets the requirements of being a safe country for refugees.
On February 8th, 2007. See this statement in context.