New-home construction calls for bringing in skilled workers who, as part of doing their job, might sustain injuries. Whether you, as the homeowner, are responsible for a work-related injury has a lot to do with whether the injured worker is employed by your general contractor or a subcontractor, or is employed by you directly.
Virtually all employees of profit-making businesses, and most employees of nonprofit organizations, are covered by workers' compensation insurance. This state-run program is funded by employers, and provides medical coverage and other compensation to workers who are injured on the job, regardless of their or their employer's negligence.
Some states provide limited exemptions allowing certain employers (such as sole proprietors) to opt out of the system. In most states you can assume, however, that anyone working on your house is (if employed by a licensed general contractor or subcontractor) covered by workers' compensation.
If you have hired an unlicensed contractor or subcontractor who is not covered by workers' compensation, it's a different story. In this situation, you may be deemed to be the employer of any workers who are working on your house at the general contractor's direction. Regardless of the general contractor or subcontractor's illegal behavior (your state's law in all likelihood requires a general contractor or subcontractor to be licensed in their respective trades, or as homebuilders or remodelers), you might be liable for a worker's job-related injuries, regardless of whether your own negligence was a factor in the injury or accident.
Any worker (including the general contractor) whom you have directly hired to work on your house is your employee, and thus not covered by workers' compensation insurance. So if you are actually negligent or reckless in, say, maintaining a safe work environment, you might be liable for a worker's injuries. (Your state's tort law will dictate the nature and extent of your liability.)
Moreover, you could be liable for negligence even if workers' compensation covers the worker bringing suit against you. Workers can sue "third parties" for injuries not covered by workers' compensation, even if they can otherwise claim under Workers' Compensation. You, potentially, are such a third party; for example, if you were to fail to clear an adjoining sidewalk of snow and ice, causing a worker to slip and sustain injuries.
Ideally, both you and your general contractor will want to have policies of general liability insurance in place before the project begins. (Such insurance covers anybody, not just workers on the site, and is a normal business expense for a reputable general contractor, who should be willing to show you a copy of his or her general liability insurance policy upon request.)
If a bank is financing your homebuilding project, it will almost certainly put a policy of general liability insurance in place at the inception of construction. The bank's policy will cover only the bank, however, so you will want to ask the bank to name you as a covered insured. It should be willing to do so, upon payment of a small fee. Otherwise, you will need to deal directly with an insurance agent that represents insurance companies offering policies that cover injuries sustained by anyone on a job site.
No prudent homebuilder or homeowner wants to be exposed to a suit for damages that might well exceed the value of the new home itself. Regardless of whether workers' compensation covers some or most of the workers on your worksite, and regardless of what kind and how much general liability insurance your bank has in place, it's wise for you to either secure coverage under the bank's insurance policy or obtain your own. Also double check on whether your contractors are licensed, and do your best to maintain a safe work site.