We can still feel quite confident that when polling finds that more than 55% of Americans agree on something, then a majority almost certainly do. (Note: additional potential errors from question wording and other areas where polling has erred such as volunteer work can add even more uncertainty.)
Indeed, approximation is what polling should generally be used for. I noted throughout this past election cycle that Biden and Trump were within the “true margin of error” of each other. That is, the error necessary for Trump to win has occurred more than 5% of the time in past elections.
We may have gotten spoiled in some recent years with how close polling came to the outcome. The national polls differed from the final outcome by about a point in both 2004 and 2008.
Historically, however, polls can be much further off.