Making Craft\DateTime Object from string in Twig
Unfortunately, what you're trying to do, is not possible without writing a simple plugin to return a Craft\DateTime object that the day picker can work with.

The global variable now, is a Craft\DateTime object, which the date picker is happy to work with because it can call localeDate() on it.

However, anything returned by date or date_modify twig filters, will be a \DateTime object, which lacks functionality that the date picker relies on.

Your only option would be, to create a simple plugin that can take your date parameter, and return a Craft\DateTime object, which you can pass as a value to the date picker/date macro.

This is one of those things that you think, "this should be easy or at least possible", but I haven't found a twig-only solution yet.