Currently silver tier Vine members get 3 picks per day, and gold tier members get 8 picks per day.
Picks reset at midnight Pacific time for everyone.
This can cause confusion for people who are in the Central, Mountain, or Eastern time zones if they use leftover picks from the day and order things between midnight local time and the reset time. In this scenario, if they go on to use all of their picks on the following day, their Orders page will show that they ordered more than their daily allotted number of picks on that date. In reality, those extra picks are accounted for in the previous day's allotment.
As an example, people who are in the Eastern time zone can use their allotted picks (8 for gold members, and 3 for silver) between 3:00 AM and 2:59 AM before picks reset again at 3:00 AM Eastern time.
Picks reset at midnight GMT. 1AM during British summer time.