I can answer for Latter Han, not for Former Han, using Rafe De Crespigny's Fire Over Luoyang. How much the Han could, in theory, pull in is disputed as scholars dispute what was the norm for tax ratio and how much, given difficulties in collecting tax, was pulled in with only fragments of information surviving.

With agriculture a key part of Han China society and arable land counted as just over 300,000 square kilo-metres/120,000 square miles, it was a key source of government revenue via land taxes. It was a blunt instrument, you had land so you made payment depending on the size of land with no attempt to base it on the quality of land (not when it came to taxes anyway), nothing changed to relate to crop yield or misfortune unless a specific remission was given. A poll tax of 120 cash for adults up to fifty-six and merely twenty-three cash for children between seven and fourteen, able-bodied men paid 300 cash to pay for someone else to fight in frontier services. Plus taxes on goods and property then eventually getting money from the wealthy by sales of officers and honours.

So what would go wrong? Some simply couldn't afford the poll tax and the likes when times became rough or when they couldn't exchange goods at the prices required, those without the protections of a patron now finding it difficult might sell up or turn to a powerful landowner who could offer protection. The landowners could take up the taxes of those under them so the poor farmer or client had that responsibility lifted but would be paying a lot to their landlord (which the government would not be getting their hands on).

Those who could afford the levies and taxes were not always rushing to pay their dues, wealthy landowners with tenant farmers and retainers under them, instead of expanding their land wealth and their wealthy estates as poorer farmers fell under their protection and sway. The landowners, very wealthy, with armed retainers and considerable influence in the area... may not always have fully declared the number of people they had under them or the full quality of their land while they could also negotiate only paying partial funds that were due.

Those enforcing it had problems, a magistrate might well have ten thousand households to be keeping an eye on. Local officials, often from the same families they were meant to be keeping in check, would be under pressure from powerful local magnates not to upset things by looking too closely at their wealthy friends or patrons.

The higher officials of the province brought in from outside the area would be relying on said local officials and were often from families of similar backgrounds as the gentry figures while knowing what was going on back in their own province. How much trouble did you want to cause by major investigations into how much the rich powerful families, who could create trouble for you be you local or an outsider with armed men and their influence, really owed? Maybe keep the powerful onside, serve your stint with as few complaints or problems of the armed kind as possible and nobody would look at your family tax affairs. They could keep pressing the less wealthy to try and make up the tax losses but that might also create problems of revolt, flight or seeing them go to the same landowners who weren't paying their full share and driving the people to revolt did not look good.

Meanwhile, there was the issue of people fleeing wars and taxation in the northern regions across the Yangzi where central government control was even weaker. The Han's cultural grip in the area strengthened with colonization but they were still not keen to be around when tax officials came and there wasn't a strengthening in the number of officials to match the influx.

When the government did raise funds off the landowners, taking from private grain stores to help alleviate crises in Ji in the late 150s, Emperor Huan's emergency farm levy, or Emperor Ling going to unusual lengths with the way he implemented the old trick of selling ranks, the Han discovered there was a lot of cash and grain lying around. Millions and millions of cash for people wanting their turn as Excellency for example. The dynasty however just couldn't get at the gentry families wealth via normal means.