Not necessarily. You have to look at votes a bit more cynically. There are generally no surprise votes in the house and senate. A 51-49 vote that passes may actually have a lot more people who would vote "yes" if they had to, but some can vote against to pay lip service to their constituents. They can go back to their district and say, "I tried to stop this bill" when they knew it would pass. Votes are regularly trade on this bases. Sometimes a party is ok with a bill not going through and "just enough" will defect from the party to kill it. Note how many votes in the senate are decided by a single senator -- even in years when the senate is not so closely divided by party. They know the numbers before it comes to the floors.

With such overwhelming numbers, presumably it could pass a veto if they had the political will. Or they can just throw their hands up and say, "we tried, it's not our fault it didn't pass." Or some nuance in the bill will come out that makes in "unfeasible" to pass in the veto override. Then it goes back to committee never to be seen again, and definitely not in passable form.

In short, don't view the vote on a bill as strictly a popularity vote on the bill's merits. Every actor involved has their own agenda, and to some, voting on the bill is just a way to build a favor or pay back a debt.