What is the function of these prepositional phrases coming after V+DO?

I would like to know what structural elements (form) would you consider to describe the function of the prepositional phrases in these sentences:

Chris Christie’s announcement Tuesday cleared the field of a hefty obstacle. This will likely nudge New Hampshire’s first-in-the-nation primary into early January.

My focus is basically on “of a hefty obstacle” and “into early January”.