4 basic categories of "atomic" weapons
Meaning weapons that use radioactive material.
1) Thermonuclear device -the H-bomb - fusion technology
very unlikely to be developed and used by terrorists, possible use if acquired as an operable (or repairable) unit - "The Sum of All Fears"
2) Nuclear Device - A-bomb - fission technology
unlikely to be developed by terrorists, but likely to be provided to them by "rogue state" regime.
3) Criticality device - mechanically much simpler than a bomb, in fact what can happen if the "bomb" is a dud. Not explosive like a bomb, but generating up to a few thousand degrees of heat for a brief time, and lethal levels of radiation, which can last for some time, depending on a number of physical factors. Very easily constructed with sufficient fissile material.
4) Dirty bomb - conventional explosive technology, using radioactive materials in bomb casing, to be spread by the explosive. Very constructable by terrorists, if they are provided with radioactive material. And not requiring the fissile material. Nuclear "waste" material would serve.
Neither of the last two will have the impact of the first two, as they are not atomic explosions, but a criticality device can kill a number of people, particularly if properly planted, as it could be constructed to emit only radiation, and thus be virtually undetectable without radiation detection instrumentation.
A dirty bomb could contaminate a multi block area, possibly with dangerous levels of hazardous materials, requiring an intensive, and expensive decon effort, but nothing that is technically difficult.
Creating (refining) the material for an atomic bomb is both simple and complex at the same time. Fissile Uranium is a naturally occurring isotope, but it is only about .7% of natural Uranium, and is distributed throughout the non-fissile material. And it is not separable by chemical means. What this means is that not only does one need the appropriate separation technology, but one has to process approximately two tons of pure natural Uranium to obtain enough material for one Hiroshima size bomb. A much larger amount of Uranium ore would be needed, and purification and refinement of the fissile material, is a complex task, beyond the capabilities of a terrorist group, but not beyond the capabilities of a nation state. India, Pakistan, N.Korea have all managed this feat, Israel is reputed to have nuclear capacity, and of course, the current bogeyman is Iran.
Whether or not the terrorists have the will to use the "bomb" if they get their hands on one is, I believe without doubt. Their biggest problem will be deciding amongst themselves which target to hit.
There is one thing that might stay the hand of the terrorists, and it is not the fear of death, or of our eventual response, but that such an act would be an abomination in the eyes of God. However, since we cannot count on them believing that such an act would be an abomination, and in fact they might believe such an act was not only justified, but was demanded by God, we must consider that there could be a nuclear weapon used in the future.