Contra /u/caustic_banana I would submit that while some grumbling about the monumental building projects, especially those thought to be excessively lavish, existed, opposing them generally in concept was unrealistic and is not well evidenced in the texts. The vast majority of the urban population consisted of poor, unskilled day laborers, whose livelihoods and the survival of their families depended on their ability to find gainful employment on a day-to-day basis. With no skills or trade they could hope only to serve as manual labor, often migrating seasonally with the harvest to and from the more agricultural suburban districts, a pattern that was still common in Italian cities until relatively recently. As seasonal agricultural labor they were important commodities--Cato expresses a preference for taking on additional free laborers during the busy harvest, so as not to feed extra slaves during the less productive months when their labor is not needed--and they made up the bulk of the city's building force. Building projects of every shape and size were everywhere in the city, comparable only perhaps with the constant construction that plagues Manhattan. Monumental public constructions in particular employed tens of thousands of individuals for months, sometimes years on end, providing secure lodgings and income for enormous bodies of the urban plebs. Indeed, the importance of the monumental building projects in the Roman economy was such that in a story related by Suetonius (the consequences of which are much-discussed) Vespasian--himself rumored to be a descendant of a man who facilitated the seasonal migration of Umbrian free workers into Sabine country for the harvest--refused to employ a newly invented labor-saving machine in transporting materials to his building projects, on the grounds that the urban plebs would be unable to find employment and would starve. Whether funded by the state or by private individuals, the monumental building projects had to exist. And this was well known even relatively early in the Republic. Private individuals, endearing clients to themselves and in order to display their public identities more prominently, funded massive building projects throughout the city and Italy, at great cost to themselves. Among Augustus' many proud boasts in the Res Gestae are his mention of his many building projects, accomplished mostly at enormous private expense (much of it of course taken in the civil war!), and Augustus notes proudly that the land on which he built the temple of Apollo was purchased from its private owners. The multi-faceted importance of monumental building projects was so great that it was even an expected service for public magistrates to go to great lengths to fund these projects at least in part from their own fortunes--the high cost of magistracy was, in the Republic at least, no small cause for grumbling among the senatorial class, but a burden which ultimately was voluntarily chosen. I would dispute that the inheritance tax on the senatorial class had any particularly profound effect on the public treasury, at least not in the early days of the Principate when land-holding citizens were almost solely of Italian and Roman ancestry. Monumental building projects were funded, almost exclusively, by private funds and war spoils. In any case during the entirety of the Republic (during which there was no inheritance tax) and much of the Principate the total value of the inheritance tax could not have rivaled the value of provincial tribute. Tribute was levied on non-citizens exclusively, and the vectigals only were levied on individuals participating in activities (mainly trade) on which such duties were placed--the inheritance tax is noteworthy as a point in Roman tax law because it was a vectigal levied on landholding citizens despite their lack of involvement in trade and import. Caracalla's extension of citizenship to the free population of the provinces was, insists Cassius Dio, in order to extend the profits from the inheritance tax, which Caracalla doubled as the mechanisms of provincial tribute were modified (starting with Marcus Aurelius at least some newly-admitted citizens still had to pay tribute). But prior to this the proceeds of the inheritance tax could not possibly stand beside the enormous value of tribute, which beginning with Augustus was no longer collected by private contractors but by a highly efficient, almost quasi-military organization. While grumbling about the excessive lavishness of some particular projects occurred--though it is relatively rarely mentioned in the texts--the monumental building projects were more than just a sink for the public treasury. Indeed, the same senatorial and equestrian elite which might have complained about their inheritance duties being used to construct public buildings spent inordinate amounts of money funding their own rival projects in the city, throughout Italy, and even into the provinces, where increasingly in the Principate entire towns could be constructed or rebuilt from the generosity of individual patrons

There certainly were, as the taxes to pay for these were generally levied heaviest against people we would call "the senatorial class", or families of that general standing. Assessing high rates of tax against these families was a way for despots to keep them down.

Rome didn't really get a handle on this until Diocletian, whom dictated a lot of reforms to taxation and government in Rome including formalizing how to tax estates. By converting to a system that accounted for average cost to feed a soldier for a year, estates could be properly measured for tangible output and therefore taxed at a commensurate rate. But, Diocletian didn't come around until 284, at which time many massive projects like The Colosseum were already long since complete (70 CE)

EDIT: I should have clarified that my response was best phrased in the context of "rich people like to keep their money" rather than actual political opposition in any sort of organized or meaningful way. /u/XenophonTheAthenian 's reply goes into excellent detail.