While reading a little about it, it does not seem that the Baltic SSRs acted in a fundamentally different way than the other breakaway Soviet Republics, by trying to progressively assert their sovereignty starting in 1989-1990. However, while the USSR seems to have mostly let the other republics go as it was collapsing, it actively resisted the independence of the soon-to-be Baltic States as late as 1991, leading to actions such as economic blockade followed by military action in Lithuania and Latvia. Was independence of the Baltic Republics viewed as more avoidable than for the other SSRs, or was it considered more of an existential threat?
The Baltic States were granted independence following the Treaty of Versailles in 1919 and saw themselves as independent nations from that point on. They were only absorbed into the Soviet Union against their will as a part of the Nazi Soviet Pact of 1939. The Red Army took control in 1944 and the Baltics states remained in the soviet union following WWII but they saw the Soviets as occupiers rather than rightful leaders. These states were not as culturally Slavic as other soviet republics and maintained strong national identities.
Following Gorbachev's reforms in the mid 1980's, the Baltic states were among the first to take action to break away from the Soviet Union. By 1987 calls for more sovereignty grew and popular national movements were gaining momentum in the Baltic states. Mass demonstrations took place often in the form of traditional song festivals. In August of 1989, on the 50th anniversary of the Nazi Soviet pact of 1939, a two million person human chain was formed linking the capitals. Globally this brought attention to the legitimacy Soviet rule and further galvanized calls for independence and solidarity among the Baltic states.
Lithuania was the first Soviet Republic to declare independence from the Soviet Union on March 11, 1990. The Kremlin instituted the economic blockade in hopes of forcing them to rescind their call for independence and squash the populist movement. Lativa and Estonia, in an attempt to avoid sanctions, decided on a stage-by-stage move towards sovereignty but the Kremlin cut back on energy and supplies anyway. Gorbachev saw the moves as illegal and claimed the nations were acting "against the rights and interests of other subjects of the Soviet federation."
Demonstrations against the Soviet Union continued during 1990 and into 1991 in all 3 Baltic states as the Soviets worked to stop these republics from being the first to break away from the Soviet Union. National Salvation Committees made up of ethnically Russian and pro communist sympathizes emerged to challenge the nationalists but they were unsuccessful as these groups were much smaller minority groups compared to other non Baltic Soviet Republics. After the communist hardliners failed in their coup to oust Gorbachev in August of 1991, Moscow formally recognized the independence of these nations in September of 1991.
sources:
GORBACHEV CONDEMNS BALTIC MOVE - Washington Post May 15,1990