Want to avoid another protracted government shutdown fight? (Given how much damage the GOP self-inflicted the last time around, I can understand why the answer might be "no", but for the sake of argument, let's assume you are more concerned with the good of the country than with benefit to the Democratic party.) The answer is simple. Quit trying to soften the blow!
You wanna shut down the government as a way of forcing the administration (and the majority of voters) to succumb to your unpopular priorities? Fine. Shut it down. But no more of this namby-pamby "essential functions" crap. The entire government is essential to somebody dammit, and just because the recipients of some parts of its benefit don't have high-powered lobbyists doesn't make those programs less important. More so, if anything.
No more solomon-unlike judgements that give us functioning air-traffic controllers for the wealthy air-traveling public, but no TANF or SNAP supplements for those who are in danger of going hungry, rather than merely being inconvenienced. No more photo-ops demanding we reopen national monuments, while babies go without crucial nutrition without WIC-provided formula. Who gets to decide which parts of the government are important enough to carry on and which aren't? The only fair answer is "no one."
On the day the budget authorization expires, ALL functions of federal government need to cease. No exceptions. No mail service. No air-traffic control. No FBI, CIA, NSA or ATF. This includes the military. No federal government means soldiers stand down, regardless where they are stationed. Stuck on a ship at sea? Guess what? You get a day off. Not so much as one bullet gets fired, one meal gets served or one wrench gets turned at any US military installation anywhere in the world, period. Same goes for VA and military hospitals: The day the government shuts down, patients will wake up in dark wards on silent floors of dormant facilities. Shout all you want, Dad, not so much as an orderly is going to show up to change your bedpan.
Won't people die? Of course they will. Probably a lot of them. That's the point: the US government is essential for matters of immediate life and death as well as matters of convenience and appearance all over the world, all day, every day. We don't get to pick and choose which ones we want to fund and which ones we don't. Or rather we do get to make those choices. We do so rationally and systematically in our budget process, and we elect legislators and executives who (we hope) share our priorities to take part in shaping those decisions. It is a messy, unwieldy and unsatisfying process, but you don't get to rush into the room with a metaphorical gun and short-circuit the system just because you don't like the end result.
The same thing goes for the debt-ceiling. If we are allowed to hit that arbitrary limit, the next day there should be no payments from the federal treasury AT ALL. To anyone. We know we don't have the technical expertise to reliably prioritize so-called "essential" payments at the expense of less crucial ones, and even if we did, we have already demonstrated we are incapable of doing so philosophically. So we simply say, "We don't have enough cash to pay everybody, so it is only fair that we pay nobody." Would this crash the US economy? Almost certainly it would, and quite possibly that of the rest of the world as well. Again, that's the point.
The Senate should immediately pass the "Call Your Bluff" Act, and demand that the House take it up as well. You want to threaten to close the government? Fine. Here's what closing the government means: No government functions, no government employees working, and by the way, no "retroactive" pay for "furloughed" workers when it's over. You want to threaten the full faith and credit of the US Treasury? Fine, but know this: There will be no asterisks, no gentlemen's agreements, no wink-wink, nod-nod, don't worry, we'll make sure the right people get paid. No. If a shutdown means a shutdown, and a default means an actual default, I guarantee neither one will last 24 hours.