Matthew Yglesias thinks so. "An agreement on a Continuing Resolution ought to also increase the debt ceiling," he writes. "Letting Republicans 'back down' on funding the government only to pick a brand-new fight with higher stakes over the same issues two weeks later would only deepen the chaos and uncertainty." MSNBC's Ari Melber made a similar argument on Twitter last night.
I'd look at it a bit differently. If Democrats accept anything other than a "clean CR", it needs to include the debt ceiling. But if they get a "clean CR" -- which is to say, if Republicans fold entirely -- I'm not sure it matters, and I could even see the demand backfiring.
A "clean CR" will be the GOP admitting it can't endure the pain of a government shutdown. If that's the case, then Republicans definitely can't endure the agony of a breach in the debt ceiling. They know that. The media knows that. And the Democrats know that. So in a world where Democrats refuse to negotiate over the shutdown and win, there's reason to be confident that if they refuse to negotiate over the debt ceiling, Republicans will fold on that, too. And winning both fights after holding to a strong no-negotiations stance would be an important precedent.
The counter-agument here is that it's better to be safe than sorry. But it's not obvious that demanding a debt-ceiling increase is all that safe. Right now, the Senate Democrats are simply refusing to negotiate with the Republicans until they reopen the government. They're insisting on a clean CR. Adding a debt-ceiling demand to that would be seen as opening a kind of negotiation. It changes the politics in unpredictable ways. It's not clear that's preferable to setting the precedent that Democrats simply don't negotiate over shutdowns and debt ceilings and that Republicans eventually fold.
All that said, if Democrats do end up negotiating a larger deal around the CR, then it should definitely include a debt-limit increase. But as of now, they're emphatic that they won't do that, at least not until Republicans agree to reopen the government.