This actually came with the Jawbox update. And, you can cycle through daily mission options by turning down the mission and speaking to the person again (just like the daily missions from the guy at the start of Crux Prime). Note that this feature does NOT apply to Sensei Wu, for some reason.
Missions I've seen so far (a * means I have completed it, a ^ means I've gotten it but not completed it):
Get a total of 500,000 points in Cannon Cove.
Get 75,000 points in one round in Cann Cove.*
Smash 5 Fire Hydrants and 10 Flowers, and build the bridge in Pet Cove.*
Smash X Doghouses and X fenceposts, and build 3 Birdhouses in Pet Cove.* (Need to check the numbers)
Smash 10 Smashables on Vertigo Loop racetrack.^
Smash X guard rails, X fans, and X lasers on the Monument in Avant Gardens.^
There is also
'Smash 10 Stromlings, 5 Mechs, and build 5 turrets in Avant Gardens'
'Smash 10 Stromlings and 5 Mechs in the Battle of Nimbus Station'
Hamsterman