Phil Spencer was the person to step up and speak about the progress that's currently being made for the backward compatibility feature.
When asked about whether Xbox would make any announcements about original Xbox compatibility, Phil Spencer responded by saying "I hope to bring more on Original Xbox backward compatibility this year, yes."
By this comment, it sounds like the feature is still in the works and it may be some time before it's finalized. There may be some blocks that could potentially slow down the project, but if we're fortunate, we may get more finalized details about an expected release date for the feature before the end of the year.
It's already been previously confirmed that original Xbox games will run better and look nicer on the Xbox One. While games won't have texture overhauls, their frame rates will be improved thanks to the increased performance of the Xbox One over the original Xbox.
There will be a library of games available for original Xbox compatibility, starting with Crimson Skies and Fuzion Frenzy. The library of compatible original Xbox games won't be as extensive as the Xbox 360 compatible library, but it'll without a doubt feature some of the most popular original Xbox titles.