Is it a bad idea to wrap christmas presents I’m bringing on a plane to the US?
I travel to and from the US a dozen times a year and have only had my hold baggage opened once in the last four or five years. You’re probably safe, but there’s nothing to stop the TSA from ripping the wrapping off you presents if they feel inclined.
Yes.
You run the risk that the checked baggage could be tagged for internal inspection. If that happens TSA will probably open the wrapped package.
If the wrapped package is part of your carryon, you run the same risk.
My parents have travelled from Canada to the U.S. for Christmas many times, and they always leave the presents they were bringing with them unwrapped. The reason isn’t so much the TSA—as the previous posters have noted, actual inspections of luggage aren’t all that common—but the customs folks. If the customs folks decide that you need further inspection for whatever reason, you might end up having to unwrap all of your gifts to satisfy them that that brightly coloured box contains a $50 Gameboy game and not a $1000 pair of diamond earrings.
Leave them unwrapped. Wrapping paper is cheap and plentiful here in the U.S. this time of year. 
Gadai, if you’re on a direct flight from Dublin, I suspect you’d be okay. AFAIK, if there are any problems, Customs on the Irish side will ask you to open your luggage and any wrapped gifts in your presence. If it happens, the worst case scenario is some re-wrapping on the US side.
However, if you’re taking an internal flight in the US, TSA can open your luggage and confiscate whatever they don’t like the look of.
See this thread.
You don’t say what the presents are. Personally, I’d leave it all unwrapped, but especially anything that has a chance of showing up on an xray.
Anything with much metal (I had a model tractor once cause a bit of a problem). Leaded glass. Any kind of electronics.
Mainly cds, some books, a teddy bear is what I’m bringing. Stingy McScrooge that I am.
Gee, just wrap them and if they get opened during a search, wrap them again. What’s the big deal?
I’m just curious. I don’t wanna go pissing anyone off who has the right to keep me out!
How about wrapping them in a box with a lid, and wrapping the lid separately? That way, they’re still wrapped, but can be easily opened for inspection.
Which reminds me of the time I woke up before everybody on Christmas Day, unwrapped all of EVERYBODY’s presents, and then rewrapped them before anybody else woke up. 
I wrap mine and put them in a second suitcase and check them. I’ve never had a problem. But then I’m flying within the States so there’s no custom inspection.
I realise the TSA has the right to rip them all open, but they never have. If they do this year, I’ll report back and let you know.