Looking at the Real Clear Politics tally of the popular vote from the primaries. Clinton has had 57.4% of the popular vote in the contests so far. Not included in the total are caucuses like Iowa which only report the county delegates that are selected. Utah's caucus was a quasi primary where participants filled out paper ballots so they are included in the total. The relative size of the caucus states not included (many of which Bernie won in landslides) is relatively small and would not narrow this gap appreciably.
The national nature of these polls should include many states that have already voted at a time when Hillary Clinton had a 10 to 20 point lead in the national polls. An interesting question is how have voter preferences changed in those states since their contests. Is there buyers remorse among the Hillary voters? Another issue is how many of these voters were unable to vote in their states such as those in Arizona and New York due to either stringent laws or inadequate polling facilities. Many polls in the states yet to vote still show Hillary with a lead which seems to lend credence to the buyers remorse argument. These issues have yet to be resolved and I haven't seen documentation in the polls to answer these questions.
These issues could spell trouble for Clinton if she were to win the nomination and/or the election making it hard to govern. The conditions could still be ripe for a primary challenger in 2020.