It's not smart to give 'any old excuse' as a reason for the delay. There's probably a pilot, mechanic or ATCer in the back who will call bullsh1t.
Part of respect for the passenger is to, within reason, simply and frankly inform them what is going on, being careful not to cause undue alarm to nervous pax.
Give an estimated fix time, but emphasize it is just a guess or you'll be held to it as 'just another lie' if the fix doesn't happen on time.