Tenured staff are virtually impossible to fire, why is the urge to find funding so strong? For post-docs and other untentured scientific staff I can understand, for their job depends on it. For a tenured professor it would rather be the joy and honour of doing important research. Apart from a reduction in joy and honour, are there any consequences if a tenured professor fails to get grants?
In many departments, tenured professors can use bringing in external funds to the department as a means of "buying" their way out of some of their teaching and administrative commitments. Similarly, other departments might use additional committee assignments and teaching loads to "punish" people who don't bring in grants. They may also have less flexibility in selecting teaching assignments.
In other countries, such as Germany, a long-term shortage in funding can lead to the consequence of a chair not being "succeeded" when the holder retires; in that case, the institute (equivalent to a US group) the professor is in charge of is wound down rather than finding a new leader for the group.
Most tenured faculty enjoy research (else why would they take a job that requires it?) and most research costs money. In particular: Faculty who benefit from working with students (or postdocs, or staff) need money to pay them, and faculty whose research depends on specialized equipment or travel need money to pay for it.
This is the carrot; @aeismail is describing the stick. I imagine both motivations can be found at every institution.
Tenure implies you're difficult to fire. It doesn't say anything about needing to pay you. @JeffE described @aeismail's answer as the stick, but there's a bigger one. Especially in soft money positions, a significant portion of your salary, much of the funding for your lab, etc. all come from grant funding. While they might not fire a tenured professor who isn't "pulling their weight" with grant funding, they may find themselves losing lab space to better funded or new faculty, not having the resources to maintain a functional research group, etc.
As long as you're comfortable with you, your office, and whatever salary is hard money being the entirety of your research group, you don't need to ever find funding. But if you want more than that, the money has to come from somewhere.