For many years, such an aircraft as descirbed was, indeed, considered to be the future of commercial aviation. In fact, Boeing took quite a gamble when they designed the 747 as some professional opinion at the time saw subsonic airliners as being on their way out of fasion. In fact Boeing specifically designed the 747 to be easily convertible to a cargo aircraft come the demise of widebodied airliners. The problem with speed, though, is the price that comes with it.
Firstly, the engines powering the widebodied airliners of today (the Airbuses, Boeings, and McDonnell Douglases, etc.) are not suited to supersonic flight. Airliners use turbofan engines, as opposed to turbojets. The turbojet simply takes in air, compresses it, heats it up, and spews it out the exhaust, creating thrust in the process. The turbofan is just like the turbojet except that it has an extra set of blades (the 'fan') set in front of the main jet engine that pushes air both into and over the turbojet part of it, acting in large part like a propeller. The fan actually provides almost 70% of the thrust in some turbofans, and makes the engine much more fuel-efficient and cooler to run. The problem with the turbofan is that it relies of taking air in at about the rate of travel of the aircraft, and pushing it a little faster. At mach speeds (the Concorde's speed range - faster than the speed of sound) the inflow of air to the blades of the fan would have a similar effect on them as applying a brick wall to a car at some significant speed. Some fighter aircraft do have turbofans that are used above Mach 1, but these are the exception rather than the rule. The turbojet can get past the problems of the turbofan at high speeds by means of not needing a very fast intake of air to acheive high-speed output. The Concorde, in fact, used variable-geometry engine air intakes to ensure the airflow to its turbojets never exceeded 300mph. But now to get air to go from 300mph to over twice the speed of sound entails some rather rapid expansion of the gas, therefore a very hot combustion chamber, and therefore very high fuel consumption (a very bad omen in todays 'green' world) added to high costs for manufacturing the engine. Also, for most turbojets to reach supersonic speeds requires the use of an afterburner which introduces fuel to the hot exhaust as it leaves the engine, creating extra thrust, but also dramatically reducing fuel efficiency and increasing pollutant emmisions.
The other main problem lies with the structure of the airframe. To acheive speeds comparable to those reached by Concorde, the aerodynamics of the aircraft must be significantly different to, say, an A380. You will notice the Concorde's nose is significantly more pointed than that of your average airliner, and it has delta (triangular) wings rather than simply swept wings. This is, again, due to the airflow at supersonic speeds. The more the air has to be displaced to travel around the aircraft, the more effort needed to do so. Similarly, the faster the air has to be displced, the more effort is needed. Thus a fat, podgy-nosed aircraft like the 747 travelling at the same speed as a fighter has to do more work on the air to get it to travel around it than the smaller fighter does, and a 747 travelling at 2000km/h (roughly Concorde speed) has to displace air 2.5 times as fast as fast as a 747 travelling at its usual 800km/h, therefore doing 2.5 times the work per unit of time. Thanks to Isaac Newton, we can say that the air does the same work on the body of the aircraft that the aircraft does on the air, so the faster and stouter an aircraft, the stronger the airframe must be (this is why the Concorde is so narrow). Add to this the heating due to friction that the aircraft experiences during flight, and the associated expansion of the metal (the Concorde 'grew' during flight, and the SR71 Blackbird extended by about a foot at its top speed of over Mach 3), and you need a very, very strong aeroplane with heat-loss coatings and other highly advanced (and expensive) engineering marvels. To minimise airflow problems, the aircraft could fly where air is thinner, but this would necessitate higher fuel consumption for the longer climb, and the effects would not be completely avoided.
This is not to say that such an aircraft is not possible; in the '60s the US Air Force was opperating an experimental research aircraft called the XB-70 Valkyrie which exceeded Mach 3 and had originally been designed as a bomber, so could carry a decent payload (think passengers). Even today, with advances in aviation technology, ramjets and scramjets (both jets without compressor blades), supercruise, and so on and so forth, many leading aircraft manufacturers are looking at supersonic passenger flight anew. Boeing, for example, had (or has - its hard to tell which projects have or have not been cancelled these days) a project in the pipeline for a suborbital ram/scram-jet passenger carrier that could easily cross the US in an hour. As has been mentioned, though, such craft would cost a fortune and it would be very hard to get the capacity to anything like that of an A380 of Boeing 747, or to acheive the eco-friendliness of the former. Thus the operators and designers would be highly unlikely to turn a profit on such a venture - they would not make their money back.
In the coming decades, perhaps, technology will allow for a large-capacity, supersonic (or even hypersonic) airliner, but at the moment such an aircraft is just not feasible.