Twitter Embeds Not Working in WordPress 3.8

I’m having a problem after upgrading to 3.8 where Twitter embeds via URL are not working. I recently upgraded WP and my plugins, but my theme hasn’t changed.

Posting the URL of the tweet does not embed, but posting the embed code from Twitter works.

Here’s a recent post where pasting the URL of the tweet embedded the tweet in the post:

https://sdccblog.com/2014/01/under-the-tents-eisner-awards-neca-lost-small-press-and-studio-confirmations/

Here’s a recent post where pasting the URL did not work, but pasting the Twitter embed code did get it working:

https://sdccblog.com/2014/01/under-the-tents-artist-confirmations-ugly-doll-film-festival-gravity-falls-the-big-bang-theory/

Now, posting the URL of the tweet only shows the actual URL in text, but does not embed the tweet. For example, if I post the following link:

https://twitter.com/sdccgotgirl/status/423672763786600448

It just appears as this in the source:

<p>https://twitter.com/sdccgotgirl/status/423672763786600448</p>

I’ve disabled a few plugins, like Tiny MCE, my event plugin, and my MailChimp widget, but it didn’t fix the problem, so these don’t seem to be interfering with the embed.

Thoughts?