HSRP with cisco routers

Yes... but...

HSRP can only be set up on a LAN such as ethernet, not on a point-to-point serial link. if ISP A is only connected to router A, what's the point of HSRP on router B? Assuming you had ethernet connectivity to both of them, you could do what you're asking by setting up a switch with 2 vlans and connecting both routers to both VLANs and setting up your HSRP across the VLANs.

But when you have 2 ISPs, routing to your network becomes a big issue: Who decides which ISP gets the traffic bound for your network, and how is that decided? You pretty much have to use BGP if you want any control over it. And if you don't have control over it, you may have problems. But the above answers your question.

Thank you for the answer Mike. I thought HSRP will desinate one router as the main router where traffic will go over hence the issue of which ISP get's the traffic shouldn't be a problem until the router A goes down because of a down line or any other issues connected to router A. Then router B will kick in and take care of the traffic. I  wrote the wrong thing when I said I was worried about inbound traffic. I am only worried about keeping connectivity to the internet our users using the web for work and items like that. So it's outbound not in.
As for setting up a switch it's not too much of a issue. That's something I can do easily. The issue right now for BGP is it will cost us close to $10,000 a year to setup. it's either that or a router aggregator. such as fatpipe's. Thank you for your help

Well for outbound traffic the 2 routers should coordinate the default routes that they generate into your network. Or if its a very small network, you can use HSRP on the LAN side of the routers to provide a single default gateway. I don't know your design.

As far as BGP, I don't know why it would cost you $10,000 per year. It's just a routing protocol. What you do need is some address space that you own, whatever that is- even a fraction of a class C. You can get your own BGP AS number for not much money, or you may be able to coordinate using the same private AS number with both ISPs. You don't need big beefy equipment or anything- 2600s would be fine. You can tell the ISPs what routes you want- probably just a default route, and maybe the main ones that they each own. No one in their right mind would take the whole internet routing table.

HSRP lets clients the *next* hop fail over from one router to another.  So on a LAN, it can fail over the default gateway from one to another for outbound traffic.

But on the inbound side, failing over from one ISP to another (without BGP, etc) means a change of destination IP address that needs to propagate back all the way to the remote host(s) involved in current conversations.  That won't work.