There's an old saying that only two things are unavoidable: death and taxes. I think this is wrong—the two unavoidable things are politics, and it's seldom-admitted offspring, bureaucracy. (Their Titan) parent is of course economics.)
Politics: you may not like it but you can't ignore it because whenever two or more people have ideas about how to do something requiring the participation of two or more people there's going to be an argument about how to do it. Bureaucracy: because once the argument is settled you need to coordinate the tasks, and once your community exceeds Dunbar's number you need to develop mechanisms for managing work and social relationships between people who don't know each other.
It's fairly obvious that technology affects the implementation details of politics and bureaucracy (and there's feedback involved too, via market regulators and command economies). And there are scale issues too. Back in the 1670s and 1680s century when Samuel Pepys served as Secretary for the Admiralty, administration for the Royal Navy ran on a handful of staff and relied on disbursement of funds—in cash—to ships' captains to see to their maintenance and the pay of their sailors. Today it's hard to imagine a modern defense ministry running on cash-in-hand: even Da'esh have accountants and an org chart. But the ability to run a modern bureaucratic defense procurement and supply organization is required due to the capital-intensive nature of modern warfare (you try buying an Aircraft Carrier with cash) and relies in turn on availability of modern tools: not just computers, but accounting procedures, project management, quality assurance, process control, and a host of other specialities that simply didn't exist back in the age of sail. On the other hand, back in the 17th century ships and squadrons might be commanded by officers weeks or months from the nearest political point of control and operating on the basis of orders which, although obsolete, had not been countermanded (and it wasn't just at sea: for example, the Battle of New Orleans took place in 1815, weeks after the treaty ending hostilities had been signed).
So. Taking the space cadets seriously for once ...
What are the political problems that would arise from the extension of an Earth-based political framework to governance of off-world space colonies? And what kind of bureaucratic mechanisms might be developed to deal with the arising issues?
Most SF centering on near-future space colonization is regrettably polluted by rose-tinted libertarian bullshit. Let's face it: in the really short term, outposts like the ISS or a near-term return-to-Moon or expedition-to-Mars will be governed by existing legal arrangements made by the national government with jurisdiction over the crew. In practice this means the 1998 ISS agreement, the Outer Space Treaty, and customary international law. And the "colonists" aren't; they're typically highly trained middle-aged scientists, engineers, and bureaucrats-with-other-skills (note how many of NASA's retired astronauts go on to careers in space program senior management or even seats in the Senate or Congress).
Looking further ahead—by which I mean out past 2030 at the very earliest—we might see encampments with a handful of people living and working off-planet semi-permanently, along the lines of an Antarctic research station (albeit in a vastly more hostile environment). "Law enforcement" overlaps messily with psychological healthcare, and generally is a matter of shipping the unruly home for treatment and diagnosis (and, optionally, restraining them en route). Money? Hah! While informal economies eventually emerge once you have a population in double or triple digits (things like trading extra shifts worked, or food, or homebrewed moonshine) it takes a long time to get to the point where "money" is internally useful for anything other than keeping track of interpersonal exchanges of obligations. And as for "no taxation without representation", that's a really long way in the future, and becomes highly problematic when the polity of 3000 who are objecting to remote governance and taxation is reliant on a distant polity of 300,000,000 who built the metal world they live in.
But by the time we look as far as self-sufficient comet-mining or terraforming colonies, a century or two in the future, the questions of political coordination and local vs. remote administration will become pressing. And these questions also apply to long-term colonies and generation ships. Assuming the (huge) obstacles to these are overcome (notably: deleterious medical radiological and microgravity effects of long-duration spaceflight; economic framework for repaying the cost of foundation; ability to maintain a large-scale closed cycle life support ecosystem; ability to replicate all necessary infrastructure components and consumer goods; ability to care for, educate, and train new members of the population and to sustain those who can no longer work or who aren't suitable for work at core survival tasks) ... what, realistically, happens?
I have some starting assumptions. Notably: the traditional right-wing American vision of settlers in space is utterly untenable because it assumes people can "walk away" from local market failures, and that individuals are solely responsible for their own errors. Libertarianism won't fly in space where any "market adjustment" is likely to prove lethal to a significant proportion of the population. Indeed, the American formulation of rugged individualism is horrifically dangerous in such a setting: imagine the mind-set that gives rise to schoolyard shooters, and put it in an environment where the only things holding in the atmosphere are the walls.
Secondly: in the absence of magical scientific breakthroughs, getting home from a fucked-up colony will be hard to impossible. If you colonize the Gobi desert or Phoenix, Arizona, you can probably escape if you have a gassed-up SUV, some cash, and enough water. If you colonize Mars, though, you're going to need a spaceship capable of reaching orbit and at least three months (more likely 18 months) of air and supplies. That's a whole different ball game, and once you realize you're living in a failed world, you're going to be far too late: it makes the plight of the people in the European migrant crisis today look trivial. Space colonies exist, of necessity, in a kind of liminal Gene Cernan voiced "failure is not an option" territory: and this is not a good place to live, much less to raise a family and expect a peaceful retirement.
So I don't see our contemporary interpersonal or cultural relationships working. Some sort of tribal organizational structure might work, by which people could work with distant or unrelated "relatives" within a web of familial obligations; it's a way of diffusing relationships to allow larger groups to work together for joint survival. Look at parts of the middle east for cultures adapted to that way of life ... or better still, don't (if you're attached to the idea of personal autonomy, choosing your own sexual partners, and deciding whether or not to have children or how to work for yourself). I'm only half-kidding: obviously iron-age tribal practices won't help cultures in brittle, high-risk environments mediated by high technology survive ... but neither will what we've got now on the sleepwalking, neoliberalalism-dominated west.
Nor are our current political representative structures, adapted to heterogeneous nations sharing an open, relatively resilient world, necessarily going to work well in a closed system. A space colony can't afford to be governed by ideology in the absence of feedback from instrumentation. But technocracy isn't the answer either; technocracy has nothing to say by way of answering the core questions of human existence, such as "what is best in life?" much less "what is right?" And a space colony probably can't survive a revolution that turns violent.
Any workable form of government for such a fragile environment is going to have to provide mechanisms for prompt and non ideologically-biased responses to deviations from the baseline. It's going to have to provide solutions that work for everybody, because the environment is a lifeboat and if you give up on someone they will die (or worse, having no expectation of living may choose to take everybody else with them). It's going to have to provide a framework for settling arguments where there is no obvious "best" solution without pissing off one faction or the other, and a framework for orderly and non-violent transfers of power (because shaved apes are addicted to up-ending their social hierarchies). The bureaucracy it comes with is going to have to offer mechanisms for delegating authority across vast gulfs of space and time, be relatively lightweight (at least in the early decades of a colony), and should arguably satisfy Rawls' philosophical notion of justice as fairness and provide distributive justice, lest it give rise to grievances leading to instability or revolution. (As a propensity for fairness seems to be wired into primates at a very low level, running on an administrative system that optimizes for fairness seems like an appropriate way to minimize friction.)
Anyway. What other angles am I missing here? You, too, can help design a constitution for a space colony! Just remember two things: it has to be somewhere you'd be comfortable living the rest of your life as an ordinary citizen, and if you get it wrong, you can't walk away.