My payroll checks will be dated Thursday, March 12. Is the deadline for the deposit Tuesday before 5pm PST?

You got it correct, @david150.

You'll want to submit your payroll by 5:00 PM PST two (2) business days before the payday to avoid delays. 

Also, ensure the account you use in your payroll has sufficient funds. To learn more about direct deposit (DD) lead times, you can read through these great articles for the details: 

• When do I need to submit payroll to pay employees on time?
• Send payroll and direct deposit paychecks in QuickBooks Desktop Payroll

I'm also adding this article for reference in case you want to invite your employees to view their paycheck online: Invite employees to see pay stubs and W-2s online.

You're always welcome to post anytime you need help. I'm always around to assist you.