Appearing on MSNBC on Monday, Terry McAuliffe made a pledge sure to strike fear in the hearts of some Democrats.

McAuliffe, the former Democratic National Committee chairman — now filling the same title for Hillary Clinton’s campaign — told the network’s Norah O’Donnell:

We are going through to June 3rd. I know there’s been a lot of commentary — Norah, I can unequivocally tell you we are in through June 3rd.

That date isn’t coincidental; it’s the day of the last Democratic primary for the year. But McAuliffe has previously said that he doesn’t see the race going on until the convention.

It’s hard, honestly, to know how seriously to take this pledge. On the one hand, campaigns promise all the time to stay in the race until the end even when it’s clear they won’t, and this may be another example of that. (McAuliffe also asserted repeatedly that Clinton will win both the Democratic nomination and the general election — given her campaign’s dire situation, that suggests that what McAuliffe said about June 3 is spin rather than a real commitment.) On the other, if Clinton wants to go out on a high note, there are a couple of times at which she could do so, and June 3 would be a good one.

McAuliffe also said he believes Clinton will pull ahead of Barack Obama in the tally of the national popular vote. Though he didn’t address it directly when asked, when he made that statement he was almost certainly assuming that the disputed primaries in Michigan and Florida would be counted toward the total, something that seems unlikely.