How long should I wait before accepting a PhD admission offer in the US?
You should ask both institutions.

Some institutions will fast-track deciding on if they’ll accept you if you tell them you have an outstanding offer. By contacting the outstanding offers, you can probably find out sooner.

Additionally, you should contact the department that made you an offer and tell them that you’re interested and honored by their offer, but have some outstanding applications and ask when they want you to get back to them by.

EDIT: I completely missed that the title says “in the US.” As the other excellent answers have stated, you very likely have until April 15th or later to make a decision. A large number of universities (see the 2014 list here) have agreed to give all students at least that long to decide to respond.

It is worth noting that the April 15th Resolution applies to offers of payment and funding, not acceptance. However, since in the US virtually all engineering PhDs are funded, it de facto applies to admissions as well. If you were applying for an unfounded masters program, it wouldn’t apply.

Some schools give longer than April 15th to decide, while others will pressure you to accept on the 15th or soon after. So for now, I would advise you to wait. If in early April you still haven’t heard back from a school you really want to go to, I would advise you to contact them as I said at the beginning.