NASA says the best time to look will be around 1 am on the east coast and 10 pm on the west coast, with viewers in North America having the best view of the potential display.
The American Meteor Society (AMS) adds that the viewing window may be short, lasting only around half an hour.
Still, it's important to remember that there is no guarantee here. "If the fragments from were ejected with speeds greater than twice the normal speeds--fast enough to reach Earth--we might get a meteor shower," NASA says.
It adds that observations from Spitzer published in 2009 suggest that some of the fragments are moving fast enough. "This is one reason why astronomers are excited."
If we do get a meteor shower, there may be many meteors in the sky, but they will not be bright. These meteors will be relatively slow-moving and somewhat dim.
"If the debris from SW3 was traveling more than 220 miles per hour when it separated from the comet, we might see a nice meteor shower," Cooke said in a NASA blog post.
"If the debris had slower ejection speeds, then nothing will make it to Earth and there will be no meteors from this comet."
If there is something to see, it's a great night for a meteor shower, as long you have clear skies. There's a new moon, so the moon won't wash out dimmer meteors.
The AMS sums up the balance of the unknown with excitement on its site succinctly, "When viewing events such as these one should expect nothing extraordinary to happen,
but certainly hope for the best!" It may be worth getting out there and hoping you get a Memorial Day weekend treat tonight.