What if we hit our campaign goal early?
That's great - keep going!
You can consider phrasing your campaign emails as "going into overtime." For example: "We hit our goal and are setting a new overtime goal." If you organization hits its original goal, send emails to your audiences saying that they hit that and announce a new stretch goal, communicating to your readers how that additional funding will set you up for success in the new year.
If you saved any potential matching funds to unveil later in the campaign, that could be a nice tie-in "We hit this goal, now we have a new goal, and we have $5,000 in matching funds" can be an effective way to encourage people to give.