"I do not have time."
Translation:मेरे पास समय नहीं है।
I think पास is only used for tangible items. Shouldn't this then be मेरे समय नहीं है।
No. Paas is not in regards to humans but is used for objects, be they tangible or intangible. In this case, "mere paas samay nahi hai" is totally fine. Also, your sentence's translation would without "पास" would become nonsensical, something like "my time is not".