Or am I just now noticing it? Words like “kitten” and “bitten” get the treatment. Here’s a good example from Steve Schmidt: TRUMP ARRESTED? Steve Schmidt explains what comes next after Donald Trump's indictment | The Warning - YouTube
I’ve noticed that as well over the last few years. I’d heard it in the past with certain British accents but it’s new in the US, at least to my ears. I think it’s called a glottal stop.
I didn’t notice this becoming widespread, but it’s very common in the mid-Atlantic dialect (think Philly). It’s called a glottal stop. In Philly, “cotton” has no Ts in it—just a kind of grunt in the middle. We don’t find it odd (we don’t notice it at all).
Steve Schmidt was raised in Jersey, so that explains his.
As long as they don’t start striking back, I don’t care.
I think it’s pretty common here in the Midwestern US, too. People don’t generally pronounce “kitten” as “KIT-tn”, it’s more like “Kih-nn” (probably the glottal stop noted by Stratocaster).
Back where I was born it was always a thing.
When people were parodying the accents of my home area they would write things such as…
“there’s trouble at t’mill”
which was never what I heard in real life. the “t’mill” had no audible “t” in there, it was a very slight pause rather than anything voiced.
For some reason, it doesn’t bother me when I hear a Brit, but it annoys the ever loving heck out of me when I hear an American.
As a native west coast Canadian, I associate it with easterners and more specifically east coasters. My most regular exposure to the phenomenon is a tic I notice with Steve from the YouTube channel Acorn to Arabella, based in Massachusetts. I find his pronunciation of “ba’en” (batten) or “impor’ant” mildly grating. He does pronounce battery with a standard middle “T” though. I’ve had a decade of living in Toronto “Trawna” about fifteen years back, so I’m little more relaxed about regional variances.
The Channel: One Minute About Acorn to Arabella: Journey of a Wooden Boat - YouTube
Electrical Systems Vid - note “important” at 1:34 & “Battery” at 2:13: Boat Electrical Systems, First Steps - Episode 194 - Acorn to Arabella: Journey of a Wooden Boat - YouTube (vid queued to 1:33).
-DF
I would’ve embedded the vids, but apparently some of us can’t right now … Have links to YouTube been disabled?
We in Philly came by it honestly, don’t be a hater. 
FWIW, I have read where this is actually a more difficult sound to formulate that a straight-up t. So in reality, we glottal stoppers are much more ambitious and hard-working, and by extension, more virtuous. Science!
O.k. I’ll give you an exception, too!
Right on! That’s my accent too. What is curious is that the only difference between latter and ladder is that the latter has a slightly longer a sound. This is especially curious since ordinarily English speakers pay no attention to vowel length. Yet my wife readily distinguishes the two words when I speak them. Another pair like that are writer and rider, where the latter has a slightly longer vowel. But both the t and d are replaced, not by glottal stops, but by near tongue taps on the roof of the mouth. The tongue heads towards the roof of the mouth but doesn’t quite make it. Nothing like a glottal stop.
Challenge: when would you have ever used those words, latter and ladder, where she wouldn’t guess the word by context? 
Between the ladder and the step stool, I prefer the latter.
Right on is right, brother! And as long as we’re discussing Philly pronunciation idiosyncrasies, here’s two more:
Soft Ls. In the same article I mentioned they tested this by going into local Foot Lockers and asking for help finding “New Bounce” sneakers (as opposed to New Balance, the proper name). No one batted an eye or expressed any confusion.
And here’s an extremely unusual one: Philadelphians pronounce the same soft vowel differently, depending upon the word. So “sad” doesn’t rhyme with “bad,” and “dog” doesn’t rhyme with “frog.”
Heck, “can” doesn’t even rhyme with “can.” “I can do it” versus “Toss it in the trash can.” Those cans don’t rhyme.
I glottalize my Ts before syllabic N. But it doesn’t sound quite like the UK accents, where you get a very harsh glottal stop and a a clear vowel. Button sounds like buh–nnn, not buh–INN.
The reason I think it happens because T and N have the tongue in the same position, and it allows the sound to stop without having to move the tongue between those sounds. And, honestly, it sounds almost the same if I do go ahead an pronounce a soft T there. (Again, not like the stereotypical Cockney version which is very obvious.)
In short, I don’t fully glottalize my Ts before N. Just partially.
I’ve always said the two words in the OP with a glottal stop unless I’m specifically enunciating those "t"s for a reason. It’s nothing new, in my experience. I wouldn’t glottal stop a word like “bottle,” though. In American English, it is pretty common to glottalize before an /n/ syllable.
Ditto, native Chicagoan living on the west coast for 40+ years. Oddly, one daughter uses the glottal stop, and one doesn’t.
It just occurred to me that I’ve always silenced the first t in internet, and that it sounds wrong when there’s a professional voice guy in commercials that pronounces it correctly. Innernet just rolls off the tongue better.
That’s what I thought listening to that youtube video. It sounded like he was really struggling to get that word out. This is different from the “Toronto-“Trawna”” issue, because “trawna” actually cuts out a full syllable, and flows easier.