You can't do this in popular elections but you can absolutely do it in the legislature where everyone has a different constituency, policy portfolio, campaign contribution history, etc. Lieberman wouldn't vote for a bill with a public option, full stop. The math worked out such that Lieberman was necessary. Ergo, Lieberman killed the public option if there was no other Senator for whom the existence of a public option would have changed their Nay to a Yea. There was not, so you can absolutely lay the lack of a present day public option for health care in the US at his feet.
Assumes facts not in evidence, notably that there is any bill oriented to the policy objectives the ACA sought to acheive that Republican Senators would have supported at that time, and (for relevance regarding the responsibility for the absence of a public option in the ACA) that such a bill would include a public option of the type Lieberman opposed.
Republicans were going to vote against the ACA no matter what it contained. That means they had no power over the content of what got passed. Lieberman had huge power over the content.
This is one of the reasons why the Constitution and amendment process exist. The Supreme Court ruled that the passage of the ACA was technically OK (I disagree, but that's moot I guess) but they didn't rule whether it was wise.
I'm saying given the political and practical mess on this issue, it was unwise. I think partisan finger pointing is likewise a bad idea.
I don't see how it's "partisan finger pointing" to explain why the lack of a public option is the responsibility of a single independent senator. It vaguely fits for stating that the 40 Republicans were never going to vote for any form of the ACA, but that's really just a statement of fact.
...there were 40 other senators who were not voting for the ACA. The bill didn't, and still doesn't, have enough popular support. You can't blame one play on a lost game and you can't blame one voter for a lost ballot.
Doubling down on employer provided healthcare with additional mandates didn't help their case.