With the current clock settings in the U.S. the new day starts at 7 PM Eastern time. I'm on the east coast so if I play a game sometime between 7 PM and 6:59 PM tomorrow evening, I will get credit for the day played.
If I tee off any time before 7 PM and do not play again until, say 7:05 PM the next night, I will lose my consecutive days streak. You have to play one between 7 and 7. It becomes 8 PM EST, when the clocks change again in the Spring.
On the game client page (the window that opens when you click the Play Now button), there is a calendar sort of display in the center, it tells you how many consecutive days you have played along with a clock that is counting down to the next "new day". If your consecutive day number is showing a green check mark then you are good, if it shows a red check mark then you need to tee off a game before the countdown clock goes to the "new day".
Otherwise
the time is gone
the streak is over
thought I'd something more to say..............