KooyeenThat way, you don't get a "A little bit" pronounced like it's a series of spits, but you get "A li(t)l bi(t)".
Your comment reminded me of something I listened to a couple of weeks ago. (
Here's the link to the mp3 file ... warning: it's 3.3MB)
BBC Learning English has made a radio programme which consists of 12 episodes. In each episode, they analyse the way some famous non-native (but proficient) speakers speak English.
In one of the episodes, they focussed on Björk's English (I hope I got the spelling correct

) and discussed her usage of collocations and her pronunciation. I'm posting here only some sentences where she pronounces the t's the way you posted:
"only I did i(t) much be(tt)er" (around 0'20'')
"the most difficult bi(t) was to know it wasn't gonna be perfect" (around 1'40'')
"the happy song are a lo(t) lo(t) more" (around 02'05'')
"sort of before and after my li(tt)le lesson" (around 02'20'')
If you want to listen about the presenters' comments about this way of pronouncing the t's, listen to the clip from about 7'20'' to about 9'00''
If you don't want to listen to that, here's a spoiler

Their opinion is that, although some people say this is lazy, incorrect pronunciation, in fact it is a common feature among young people in London, and it clearly demonstrates that Björk has lived in England.