I would be doing long tours as much as a month or two.
It might not be all that good as a touring bike. Many cyclocross bikes do not have eyelets to mount mudguards and racks. In addition, even if they do, the chainstays may be too short to allow sufficient clearance for panniers, your heels might hit the bags with every pedal stroke. Most cyclocross bikes do not have triple cranksets, so gearing might not be suitable for climbing with heavy loads. Most touring bikes have longer wheelbases, and lower bottom brackets to provide extra stability. This is important when the bike is loaded with baggage. Touring bikes are built to be rigid enough to handle the extra weight of the gear you need to bring along on a long tour. While the two types of bikes look similar, they are not interchangeable.
I can't argue with mtlbiker's good advice, but I'll contribute some additional thoughts that might help you.
There are people that tour on cross bikes, so it's not that it can't be done, rather that it's generally not the best choice for most people taking longer tours. Keep in mind that some people are able to make long tours with a relatively light load, whether that be from utilizing motels/hostels or from the ability to do without some comforts.
The first important trait of a good touring bike is comfort. When you compare the geometry of a typical touring bike vs a cross bike, you'll see that a shorter top tube and longer head tube puts the rider in a more upright position. While it's easy to swap a double crankset for a triple, the geometry is what it is.
There actually are a number of cross frames that will accommodate fenders and a rear rack. For heavy loaded touring, lowrider eyelets on the front fork are handy for distributing the load. I believe the Tricross by Specialized has these, others might also. I've even heard of people mounting a eyelet-equipped touring fork on their cross frame but have no idea what that would do to the handling characteristics. A trailer would circumvent the need to load down the bike itself, but not everyone is crazy about hauling a trailer.
If you already own a cross bike you would like to tour on but can't drop the money on a dedicated touring rig, you could make it work. But you might not be as comfortable for long days on the road, and the handling might prove to be a chore. Loading down a cross bike and taking some long rides could help you confirm if it will work for you.
A cyclocross bike is not the best style of frame for long touring, but would likely suffice for light touring of short day trips.
The reason is not due to fender or rack eyelets, but the frame itself. Because cyclocross bikes are intended for racing the reinforcement in the frame is reduced down to the bare minimum to make it as light as possible. When you load up your bike with a large amount of weight a lightweight cyclocross frame will likely feel squirmy and wobbly. A dedicated touring frame is reinforced to support the weight of panniers and packs loaded onto front and rear racks.
Last, the angles of a touring frame are optimized so that it will feel stable and balanced even under high loads. In contrast the angles of a cyclocross bike are optimized for quick and responsive handling; a characteristic which will make a loaded frame feel twitchy and unsteady.