Most gay rights organizations have dropped their support for the current version of the Employment Non-Discrimination Act (ENDA). This version of ENDA has an explicit and generous religious exemption. This would allow employers with a religious objection to treat sexual minorities differently to other groups, such as women, even if they also have religious objections to women.
In the recent Hobby Lobby decision the Supremes said that the Religious Freedom Restoration Act (RFRA) can be applied to the Affordable Care Act. That's because the ACA doesn't have a clause saying the RFRA can't be applied.
In a similar manner the Supremes could conclude that because the exemption in ENDA is so generous that Congress means to apply that generous exemption to other gay-related laws, such as hospital visitations and spousal benefits.
It is obvious that the current ENDA isn't going anywhere in the House. But Obama is talking about doing much the same thing through executive order (with federal contractors). Gay rights groups don't want Obama to think he can lift the religious exemption language from ENDA. So they dropped their support.
My dad pointed me to an article on DailyKos written by Man from Wasichustan. He expands on an idea from radio host Mike Papantonio, which is something like this: A person or family incorporates their business to create a legal separation between the business and the owners. If the business defaults on a debt business assets can be taken for payment but family assets cannot. This separation is known as the corporate veil. Through the Hobby Lobby ruling the Supremes pierced that veil – the owner's religion and the business' religion have become the same thing. The owners are not completely separate from their business. Perhaps owners can be made responsible for the business debts too. And lawsuits making this claim will soon be filed.