I ordered something at around 7:00 pm, and it claimed to take 1 business day to ship. I know that business days are counting the weekdays, but does the time of the day effect the predicted arrival time of the package?

Will it arrive tomorrow or will I have to wait until Monday?

You stated 1 business day to ship. The site should show you if received by a certain time. 1 business day to ship does not mean that you will receive it in 1 business day. Depending on the shipping method among other factors it could take up to 5 days. Go back to the site and see what the cutoff time is for 1 day processing and shipping time is. It will be there.

business days are Mon - Fri, no weekends....if your ordered 12/18 @ 7 PM your order will be processed 12/19 and you might it on 12/22, but it could be delayed due to heavy volume of mail/shipping

Probably Monday even if they mail it Friday which is one day. This time of year everyone is busy so give an extra day.

1 day not including weekends