Our bodies are amazing things. They adapt to whatever we want to do in life without us even noticing mostly. They store the information of whatever we're doing when we're active, and when they get a chance (when we're resting/sleeping), they adapt to be able to better do that activity the next day. The harder we push ourselves, the more they adapt to be able to go that hard again with less effort.
This is what in sport we call the training effect. Every hard session you do is only one half of the picture - it will only pay off once the body has assimilated it. If the effort of our training session is well within our body's current capacity, a good night's sleep will do it. The harder we push ourselves, the more rest we need before we can assimilate the training effect.
For those of us who train for sport regularly, if we neglect to monitor our recovery properly, and just keep training as hard as we can, we will reach a plateau where we're too fatigued to be able to push ourselves hard enough to get any sort of training effect. This happens to a lot of people. We have to know that for every "quality" workout, we must put in recovery time. This means being able to measure our effort accurately so that we don't overdo it on a day that should be easy.
It is definitely possible - and in fact necessary - to push the boundaries. Subsequent hard days are great for building endurance for longer races and stage races, but we must be aware that we will need to pay back what we are using now or we will arrive at the condition known as overtraining syndrome. The first symptoms of this are irritability, poor sleep patterns, irregular bowel movement, and eventually a severely compromised immune system which means we'll pick up any bug that's going around.
These days I'm doing a lot more riding than I used to. Since I started my bicycle-touring operation I've had to be very disciplined about keeping in shape. We are doing rides from 2-7 days in duration and often including some long, tough stages. In preparation for one of these rides I'll need to make sure I have some down time before. If it's just a 2-day thing there's not that much to consider, but if it's 5 to 7 days, I shouldn't be doing too much the week before.
After a ride like this, that may have involved an average of 120km of riding daily, I'll generally take a week off from anything structured. Sometimes more. I'll probably take 2 days of complete rest, followed by some easy spinning on the 3rd day, a short run on the 4th day, and then play it by ear. It's really a chance to do other things so I embrace it (you'll see much more activity here during those times!).
Reading your body
Your body will tell you when it's ready to resume normal effort levels so you have to be attentive to signs that it still needs more time. If you have a heart rate monitor and power meter it's easy to tell. A low heart rate and power means your cardiovascular system hasn't recovered. A high heart rate and low power means your muscles need more recovery. Once your levels of both start to respond normally to increased effort, it's time to start re-introducing (slowly) some harder efforts. Pointless to do it it too soon as you'll only interrupt and then prolong the period of recovery.
Be sure to eat well during your recovery period, and forget about keeping your weight down for a while. Plenty of fruit and good complex carbohydrates, plus eggs and good lean meat, but really it's just time to enjoy your food. Don't be too anal about it.
I used to do supplements, but I don't believe in them any more. I have found it to be vastly better to eat properly and get all the nutrition you need from real sources. For a start, it's the way your body's built to do it, and secondly, there are a lot of things used in the synthesis and preservation of the vitamins and minerals in most supplements that are unnecessary toxins for your body to deal with. Plus it's usually an excuse to eat crap otherwise. Crap fuel = crap performance.
One of my staple recovery drinks is a blend of oranges, green apples, beetroot, celery and grapes. Don't juice it, blend it - that way you get all the fiber too. If you want more ideas on a good cyclists diet you can check out The Feed Zone by Dr Allen Lim.
If it hasn't occurred to you yet, proper hydration levels are THE most important thing to ensure continuing good health and a strong immune-system. I can't state this emphatically enough. Since I started forcing myself to super-hydrate every morning with a litre of water, I have a tiny percentage of the ailments that used to affect me. It's not the most comfortable feeling in the world initially, and you'll pee a lot, but you'll notice the difference quickly. I drink it warm as it really gets the bowels going. It's a detox and hydration cure in one. Believe me. Do it!