This is a very potted history and will no doubt contain a few over-simplifications and errors:
Franco crushed the nationalities, of which there are a few in Spain. Catalans consider themselves Catalan before Spanish, and Galicians consider themselves Galician before Spanish, but they are at least ethnically and linguistically related to the Castilians. Basques are not. The Basque language is a language isolate not even remotely related to Spanish or in fact any other language in Europe, possibly anywhere.
There's a lot of nationalist feeling amongst the Basques, which Franco attempted to quell by running roughshod over them. This led to many uprisings and protests, and eventually the formation of Euskadi Ta Askatasuna (ETA), a militaristic separatist group. They were founded in 1959, and stepped up their activities to include terrorism from 1968 onwards, perhaps influenced by uprisings across Europe in that year leading to terrorism, such as the Baader-Meinhof Gang/RAF in Germany. Over 800 people have died at the hands of ETA in the last 40 years. They are also the people responsible for the Madrid bombing of a few years ago.
After Franco's death in 1975, when Spain returned to democracy, there was a period of transition. Expectations amongst the large numbers of Basque separatists were high (even though over the previous 40 years nationalist policy had seen large numbers of Spaniards move into the Basque country, similar to how Mussolini had tried to quell Südtirol's German identity by creating industrial works and bringing Italians in from afar to work there), but the area remained in a state of turmoil; Suárez refused to deal with terrorists, ETA split into a political-military and military arm, and trouble escalated. In the 1977 elections, the PNV (Partido Nacionalista Vasco) and PDC (Pacte Democratic per Catalunya) were highly successful in their respective areas, and disappointment at the failure to secure independence or in fact any higher autonomy, led them to refuse offers of amnesty, and the period 1978-1980 remains the most violent in the history of the group.
Hence, after the difficulties and protests at the 1978 Vuelta running through the area, Unipublic were not keen on offering a chance for ETA - whose activities were intensifying at that point - a golden opportunity to make a big statement. From the 1980s, ETA bombings of major Spanish cities - usually car bombs - have been sporadic, plus "counterterroristic" groups like GAL (carrying out terroristic attacks on ETA themselves) have also contributed to unrest. There have been a number of ceasefires and reductions in activity, usually with the Basque political parties being offered a carrot in some form of grant of further autonomy. However, every time peace proposals are offered by ETA or the Spanish government, some conditions are unacceptable to the other side.
The tightening of anti-terrorist laws across Europe as a result of the September 11 attacks in the US have put a lid on the extent of terroristic activities in the Basque country, which reached their zenith in 1997 with the kidnapping and subsequent murder of a prominent politician when their demands were not met.
There are also a number of non-violent and less violent Basque nationalist movements, who Unipublic feared could use sitdown protests, rioting, fighting, road blocking and so on to disrupt the race. The right to a Basque referendum, first planned in 2007 and scheduled for 2008, though still incomplete and a contentious issue, suggests a (relatively) more conciliatory attitude between the Spaniards and Basques, and with ETA activity on the wane after the permanent ceasefire called in 2006, they've decided that now might be the time to send the Vuelta into the Basque country.