The easiest and cleanest way uses the transclude widget with the index attribute to get a property from a data tiddler:

It's ''<$transclude tiddler=UsHolidays index=<<now "0MM/0DD">> />'' today!

However, we didn't discuss the transclude widget, so it's unlikely you thought of that! Here are two other ways to accomplish it; you might have come up with something yet different that also works fine.

<$set name=formattedToday value=<<now "0MM/0DD">>>
  It's ''<$text text={{{ [[UsHolidays]getindex<formattedToday>] }}} />'' today!
</$set>

(Recall that the text widget is needed to prevent the holiday from turning into a link with the use of triple curly braces.)

\define holidayTransclusion()
  {{UsHolidays##$(formattedToday)$}}
\end

<$set name=formattedToday value=<<now "0MM/0DD">>>
  It's ''<<holidayTransclusion>>'' today!
</$set>