Timing The Tet Offensive kicked off in January of '68 and carried on throughout the year. My Lai occurred in March, and didn't become public knowledge until late '69.

The American public, leading up to Tet, had largely been led to believe that the North was incapable of a large offensive - something that the DOD believed also despite growing reports of increased supplies coming from the North. When the offensive broke, it brought into question what was going on over there. Walter Cronkite's commentary in February further fueled a sway in public opinion.

The increase in combat led to a need for bodies. The draft increased dramatically, as did public opposition. My Lai served to further bring into question just what the hell we were doing over there.

The military
When Thompson initially reported the events to superiors, the investigation was never pushed. He and his crew found themselves on more and more dangerous assignments (his copilot was killed shortly after) and believed it to be punishment or at least an attempt to get rid of the trouble makers. Charlie Co. was sent into the bush for an extended period, keeping them outside of the ability to testify at great length. The initial investigation wrapped up, and the whole incident was written off.

When the investigation was started in earnest at the behest of Congress, Gen. Peers was placed in charge. Coming up on retirement, the Army expected he would marginalize any wrongdoing. Instead, he released a scathing report that laid blame straight up the chain of command - which laid the heaviest blame on people who were already dead (such as Col. Barker who headed the Task Force, and was killed a few months after My Lai).

As many if the enlisted men involved had already mustered out, and were outside of the purview of military justice, the first to be convicted of murder was 2LT Calley. He proved to be a scapegoat, as other in his chain walked away by laying the blame on him. Disturbed by both the use if Calley as a scapegoat, and a painted as a victim of circumstances, Calley ultimately had his conviction overturned by the White House after a letter campaign and public polls showed overwhelming public support.

In the end, the only ones who paid for My Lai were the civilians killed that day. Shy if being an isolated incident, it brough to public light military policies which focused on body counts instead of results (My Lai was in no way an isolated event - see Op. Speedy Express).

My Lai did establish that officers who ignored reports of attacks on civilians were just as liable as those who committed the acts - and to this end investigations are done much more often into allegations (as witnessed in Iraq/Afghanistan. But also, I wouod argue, it reinforced that blame could and should be concentrated at the lowest levels whenever possible.

PBS has a very well done documentary on My Lai that I'd suggest watching, as well as a list of further readings. Also there are PDF copies of the Peers report and Congressional testimonies floating around. The testimony's are by far the best source imo, and I would suggest reading them if you want an idea how horrorific the whole thing was. Also see Hunt - Vietnam at War, Bradley - Vietnam War Reader for background and context.