I think the answer is: it depends...
As both an investor, and a former advanced tech start-up founder (where we raised about $25m in Fed. funding), private investors look at government funding from two perspectives:
1) Non-dillutive capital: Government grants, especially SBIR and STTR type grants, do not come with a whole lot of strings attached. There is really no significant IP or commercialization entanglement with this type of funding. The Feds are investing this grant money specifically because they want to see you develop and commercialize your idea. The only issue that arises with regard to government rights comes up if you cannot or will not commercialize IP that the government has helped fund. So in this sense, government funding helps you invest in early state research and development on the government's dime. This is good for you in terms of retention of equity in your idea, but is also good for your investor, because you are not burning his or her $$ on early stage R&D.
2) The other perspective that investors should have on this type of funding relates to how much it will cost the company to pursue and execute the grants. Government funding mechanisms, especially phase I grants, can take a lot of resources to go after and they rarely ever materialize very quickly. Unless you are pretty wired with the group that will administer the grants, you can burn a lot of time writing grant applications that will never be successful. Even when you are successful, the money will take time to wrestle into place, and then there is a certain amount of overhead to administering the grant effort.
Summary: as an investor, I'd be thrilled if a company had already been awarded government grants and spent it as non-dilutive capital on R&D. I'd be ok with ongoing funding as long as it doesn't diminish the company's ability to move quickly and pivot when necessary. But, if an idea is truly appealing, I would prefer to put private capital to work instead of leashing the company to a slow government process for evaluating applications and granting relatively small amounts of money in the early phases.
Good luck to you.