No one expects the veto to be overridden. The House of Representatives passed it first, but only 265 members voted for it, which is short of the 290 needed to overturn the veto. Unless lightning strikes, it will fail there and not proceed to the Senate where an override would likely have been successful since more then 2/3rds of the Senators voted for the bill.
Now the politics begins, which some disdain, but I think it more than appropriate for an item like this. The vote was along party lines. 220 Democrats voted for it, 8 against and 151 Republicans voted against with 45 for. Voters have a pretty clear signal about how to vote if they favor or oppose the bill, which is what a two party system is supposed to do.
Polls suggest that most Americans support the proposed expansion--but this does not necessarily mean that most voters do (or that voters favor it by a similar percentage).
Republican leaders suggest that those poll results may not be accurate: "House Republicans quietly distributed a survey by David Winston, who is close to [House minority Leader John] Boehner, that came to a different conclusion. It said critics of the legislation can win the public debate if they say they favor "covering uninsured children without expanding government coverage to adults, illegal immigrants and those who already have insurance...." A copy of the poll was obtained by The Associated Press."
The key to this poll question is that it connect the expansion with expanded government, illegal immigrants, and those who can afford it on their own. Pollsters call this a framing effect--which we cover in 2301 when we discuss the measurement of public opinion. This puts a negative spin on the issue and suggests how Republicans will attempt to negate the almost certain backlash that will hit them next year.