This is such a tough position to be in, and while every dog & every situation is different, I had to make the same decision for one of my own just 2 weeks ago.
You don't mention what type of tumor is on the spleen, or the symptoms that caused you to have her checked out by your vet. Some tumors are more 'operable' than others. My dog had hemangiosarcoma, which is a tumor of the blood vessels, & the prognosis 6months post surgery was only ~30%. So we made the decision to say our goodbyes. I was very fortunate that she was able to hold on 3 extra days so I could come back home & be with her.
Here are some facts - Older dogs have a more difficult time in recovery of any surgery than a younger dog, all things being equal. Anesthesia works against the immune system, so there is a greater chance of infection post-op. Large breed dogs have an average life span of 10-12 years, making life-saving measures late in life a diminishing return in exchange for the risk.
Specifically to your situation, here is the information page I used to make some of the decisions for my own dog, & also one of my puppy owners in the past few months: http://www.veterinarypartner.com/Content.plx?P=A&A=13...
If you know the type of tumor, you can click on the hyperlinks within that article for more information regarding treatment & outcomes of hemangiosarcoma & lymphosarcoma.
You are asking for advice, what I as an owner would do. Here it is:
I would make an appointment with your vet to let your dog cross over the Rainbow Bridge. She has led a good, long, loving life with your family. At her age, the risks of surgery are great. The amount of time you might buy through a successful surgery will be limited, & also require significant recovery.
Any vet will tell you what they "can" do for your dog (or cat or other family pet). But they aren't the ones that are going to tell you what you "should" do, and that burden is so hard as a pet owner. We love them, they are part of our family, and the greatest worry is saying goodbye too soon.
But my husband & I have always said, we would rather say goodbye too soon, than too late. If our girl was 5, we would have gone ahead with an attempted surgery. But at 11 years, it just wasn't worth it to have her last few months with us not be spent in perfect health, or worse, have to lose her on the operating table without a chance to say goodbye & let her go with dignity.
All that said, if you & your family decide to go ahead with the surgery tomorrow, that is OK too. I can only share what I have done, & would do, & my reasons for it. I have a friend who nursed her dog for 3 years through a condition that is the same as ALS in dogs. I've known others who let their dogs go peacefully in the early stages of the same disease. I can't & won't judge, because everyone's situation is different, & every dog is an individual, with their own abilities to fight with a positive spirit.
So, I hope this was helpful in some way. I will be praying for you & your family tomorrow, that whatever decision you come to, it is the best one for your beloved girl. T.