Does Cisco HSRP require a dedicated Ethernet port?

I have a pair of 2801s … Each has two Ethernet ports, and no more can be added. On each router, 1 Ethernet port is used for internet, and the other to the internal LAN switch. I would like to implement HSRP, but do not have an available Ethernet port. Can I do HSRP via the Ethernet connection going through the LAN switch?

Thanks.
DJ