I originally had gone yesterday by myself (I had gotten information that you could go alone to apply for one). But surprise you can't. So FI and I went back this morning and applied. We should have it in the mail after Tuesday. No one said anything about it taking longer due to the shutdown, etc. But still I recommend just getting it done if your wedding is coming up. It took literally 5 minutes.
Side note: you need to know what your name is going to be after the wedding, something I didn't know I had to finally make a decision lol.