I can guarantee you that almost nobody in the US is worried about any economic agreement with any other countries.
if there's anything close to that with us, it's economic cooperation with japan and not the UK. The "special relationship" is posturing and and military / strategic consensus and may have some wrinkles.
when you get to the group of folks in this country who complain and produce nothing (university art professors, etc, who "worry about" what other people think about them), they're usually upset that friends in france and belgium might think something the government does is a reflection on them.
it isn't. I go to my job during the day, I spend time with my kids at night. if the government does something dumb, it's the government. If I talk to a friend in Scotland, I'm not talking to Prince William and never confuse the two.
As for services that we've had to shut down? Care to elaborate? I work with the government on a fairly regular basis (i'm in private industry). I've dealt with nothing other than a voicemail at the IRS and DOT that says that the offices are closed and to leave a voicemail. This is a departure of zero from normality because the IRS and DOT will not answer the phone when they're in the office - they just don't as a matter of policy unless you're dealing with the general number (they will answer you there and route you - if you get further in than "where do I get tax form X", they send you to the voicemail of someone you could have called directly, and that person calls you back).
That's how it works. I literally called the DOL yesterday and went through their help number (it took about 3 minutes of wait time, they referred me to someone else and i'm waiting for them to call me back.). In "normal" times, the same thing occurs. If I call a number directly and someone is in the office, they don't answer and never have (at the IRS, DOL, treasury unless you're using the general number - but again, instead of leaving a voicemail, the service representative arranges the call for you and you wait the same amount of time).
Sometimes I hear a dog or a kid in the background now, which doesn't seem that unreasonable.
We have a debt problem. Most of the world does. It seems that people dwell on it only when their favorite candidate isn't in office.
I have no idea if people in the UK think something about their government should make them embarrassed when talking to someone from the US. We don't care, so why should you be embarrassed. we don't have this weird "we're all together" association that some parts of the world have with their government, and if you try to do consensus building in the US, your idea had better have merit because you don't get the euro style "we have to all have the same answer" thing. I've noticed it with our (my, personal, not figurative) european friends - they pose something to you and they stare at you..."right? don't you agree?". What's the deal with that. There's a simple principle - we can be friends without agreeing on everything or doing the exact same things.
As to our economic troubles, I see in the last two decades, we've seen the rise of amazon, apple, tesla, google, space x, etc. Our per capita GDP is 50% higher than the UK. If you asked anyone anything over here about that, it would be a suspicion that the UK is past the point of being able to innovate and that the government do-all structure has made everyone far too comfortable by disincenting success and risk.
Ireland appears to be pretty successful at growing their economy, but it's a point of interest for us in the states and not really much of a lesson as it's about a fiftieth of the size of the US economy.
Our government has been basking in non-achievement since at least the mid to late 1980s, but the economy hasn't suffered for it yet, and I'd imagine that the accommodation of the jobless and disabled here is probably better than than most places despite the one issue americans have trouble admitting. The downside protection in this country is socialist. The one condition is that you generally cannot get it until you're actually poor (as in, you may qualify for free medical coverage, free income, free or near free housing, free food, etc, but you will not be allowed to build up a pile of assets and then get those - you are required to spend those down before the government foots the bill for you). Somehow, we've structured that without taking away the top side incentive to innovate and create economic growth, but the structure in my mind is by refusing to pay the current bill and kicking it toward the future.