As part of several quick builds in my congregations as well as a member of the finance department of two RBC's I've seen several situations of this:
1) They would send the CO to see where the problem lies. If the problem lies with the elders simply refusing to pay they would summarily replace the rebels and have the congregation back on track. I've not seen this in a monetary issue but in other issues where a couple of the BoE didn't agree with the CO/branch recommendations and they were simply replaced by the next yes-men in line.
2) If the donations are too low or non-existent, again, replace the account servant and see if the problem fixes itself (a lot of them have had sticky fingers). If not, guilt the congregation into donating more. Usually a project will have people (anonymously) writing down how much they can donate each month or as a one-time gift before the project is started. If the money is not flowing properly when the project starts running, they get frequently reminded of these promises they made. I've seen this happen in a few poor congregations quite a few times and especially the elderly would get a "shepherding visit" with the CO.
3) If the whole congregation refuses to give or do anything as a part of growing dissent within the ranks, the congregation would simply be broken apart and sent to other congregations.
I've seen this happen only once in a set of large congregations that was combined under one roof (6 congregations that previously met in 4 different buildings). The project was very expensive, very tedious, came right after major renovations to all the individual kingdom halls that were being renovated, the money for the sale was funneled into the organization and not towards the new project and the new kingdom hall was placed right at the end of an airfield's runway (very cheap property) and a quick build of a brick building in those circumstances cannot technically be sustained (and at least two worldly husbands who were contractors warned us of this) so cracks started appearing even before the inauguration.
The 6 congregations had nearly a million dollars of combined debt (the old renovations, no proceeds from the sales of their property and a completely new quick build of 2 large halls and a medium sized room for groups, brand new carpets and chairs and electronics and then a few weeks after that injections of concrete to restabilize the building and repairing large swaths of brick, facade, wallpaper, wood trim, plumbing, electricity etc.) so the congregations protested, 2 out of the 6 bodies of elders advocated no longer donating to the organization. In the end 2 CO's and 1 DO got together, the project remained in place, one congregation was disbanded, about 20 people across the bodies of elders and servants were disfellowshipped for apostasy, several of their family stayed away and the remaining congregations were simply rebalanced, the DO was promoted to a cushy Bethel job. The debt is still there and the poor chaps are still paying for it now almost 10 years later. The remaining balance is also accruing interest (as that is what happens when you don't pay your debts back to WTBTS in 10 years - they charge a fee (~10-15% of the balance) + 2% interest rate).
4) Technically they can be taken to court as they are all separate entities with their own officers etc. The Officers are supposed to toe the line of the WTBTS but if they don't (ala Menlo Park) they simply get replaced by other Officers. I posted the bylaws and instructions for those once here, you can find the documentation which outlines how those officers get chosen and how the "shareholders" are supposed to vote etc.
