The amount of money we are talking about for research is so small in comparison to the debt that it’s a red herring to even bring up the current debt level. As you’ve noted, even the largest parts of the budget are dwarfed by the total deficit. Researching is a rounding error.

There’s this thing called taxes. We’ve had thirty years of tax hawks intentionally creating this situation that we find ourselves in, because they’ve cut taxes without any sense of responsibility for its impact on the debt/deficit. In fact that’s been their plan all along, to “starve the beast”, cause a crisis, and force cuts to popular programs that they wouldn’t get political support for otherwise.

Universities could pay for all of the research themselves theoretically considering they're the largest business in most states. Their portfolio income, the sports income, the donations, and the free real estate given to land grant universities that has been heavily monetized all add up. Of course I doubt they will allocate money to research, but they could if that was truely their purpose as an organization.