first of all, what would you construct it out of? concrete you say? sorry, wrong answer. concrete piers have to be a minimum of 8" thick to support a force of 10kips. to give you an example, a bridge of 3 lanes (approx 30 feet wide) would have to be 12 inches thick, and concrete is 150lbs/cubic foot. so per linear foot in the long direction, the bridge would weigh 4.5kips. that isnt even accounting for outside forces, such as the wind, water, traffic, and the weight of the steel beams which would be located under the bridge to keep it from crumbling like a cracker. the weight of the piers, which i will explain in a minute, would also add a huge quantity of weight to each section of the bridge.
the problem with piers is that when you make them very long, the weight of the actual pier excedes its capacity. this problem can be overcome with lateral reinforcment with steel of almost an inch thick placed at 4 equidistant places from the perimeter. the real problem for support would be how to keep these piers from shearing right in half. concrete design is usually a product of many equations in statics related fields. this kind of project would most definitely be related to the dynamics part of it. keeping concrete (which undoubtedly would crack like a mother fvcker in this case) from shearing (even with steel thicker than what is on a suspension bridge) would be impossible. as a matter of fact, i designed a foundation for a parking garage a few weeks ago and in order to have it support 45kips/pier, we needed something like 20" in diameter by 35 feet deep. just a side note...finding a contracter to do this who is worthy of such a daunting task is nearly impossible. anyways, back on topic, so to use concrete would be an unbelievable waste of resources as you would have to thicken the base to several feet (as in greater than 20 feet) per pier and in order to hold heavy trucks/semi's, the piers could be no further apart than about 25 feet. obviously these are just a product of the equations and properties of concrete, so the real world variations and imperfections would change the actual strength of the bridge. now, say you used steel. first, where would you get that much steel? sure, it wouldn't crack, but it is not totally different from concrete in regard to its tensile strength. after long periods of time, steel will deflect where concrete would have sheared, but deflection in the Y, X, or Z directions would be equally as bad if something were to travel on it at high speed. this type of bridge is simply impossible to build based on our current knowledge of materials and their properties.
also, as others have brought up, this is such a long trip...you would need a place to sleep, many places to get gas, and some entertainment. personally, if this project were to come to fruition, i would need a strip joint every 500 or so miles. also, you know some asshat would terrorize this bridge in some way. surely some moron would drive a truck with a couple thousand pounds of dynamite or the likes and detonate as soon as they crossed into the USA. i think this kind of traffic flow would bring in much more terrorism because transporting "goods" would be 1000000x easier.
edit: i would never want to travel in a submarine as a form of regular transportation. i realize it wouldnt be so tight in there if all of the military machinery were to be extracted, but still, its a big tin can and people who are clostorphobic (sp?) would go crazy and sink the boat (not sure how, but stupid people always amaze us).