In events, there are two types of quests. The first type is called a 'rush quest', and can be completed immediately. The number of these rush quests is limited, and you will eventually run out of them. The second type of quest is a 'daily quest'. There are four daily quests available per every day of the event.
Once you finish the rush quests, you will likely catch up to the daily quests, but once you get to and complete your current day's quests, you will then have to wait for the next day to get more.