I think they would both work in the US, but you would need to do American versions just because shows like News aren't much fun if you don't know what the news stories are and the stories they use aren't usually world issues.
I think about this a lot. For instance, would a John Stewart work in the UK?
There seems to be this cultural thing in the UK where the discussion of politics is treated differently than in the US. With HIGNFY, they can make points but there needs to be a lot of chuckle in there or something. Almost like if you discuss politics you have to completely remove yourself from investment. Stewart goes for the throat, even if he smiles while he slips the dagger in. There is anger there.
I was reading Andrew Marr's History of Modern Britain again and he makes a point that this sort of disengagement is both a blessing and a curse. To some degree the stability of the Parliamentary system comes from the collective shrug of the citizenry, the old "Well they (the powers that be) are at it again, what can you do?" - and by extension "They are the ones who are rightfully in charge and we are the powerless masses". So while France set about beheading the rich, England stayed calm and carried on.*
To me, and this part of my ever-evolving Grand Philosophy on the State of Great Britain, I think at heart the British hold a deep sense that society still operates according to age-old societal structures. Americans think they can, and want to, change things. So our (US) political humor is that of the activist, and UK political humor runs more towards the much talked about ironic disengagement. You are thought a bit of a fool if you hold strong political beliefs (or religious beliefs or what have you).
It is seen even a bit in the way collectively the people react to mass grief. When Elvis died it seemed totally natural that his fans grieve, but with Princess Diana you see a nation very much confused about what they should do. You see it in things like the Olympics where you get this huge national eye roll whenever it is brought up. I think football is the only thing you can discuss dead seriously here.
If HIGNFY appeared in the US I think it would pretty quickly descend into rancor, and I think if a John Stewart arose here in the UK people would find it a bit too direct.
*This is of course a generalization, and Marr admits it. For instance the 1926 general strike was basically an insurrection. The fight for universal suffrage was a pretty serious affair.