Josh Chafetz, a law professor, writes in Slate:

Minority Leader Nancy Pelosi should offer McCarthy a deal: Democrats would provide the votes necessary to make him speaker and keep him in the chair for the remainder of the 114th Congress. In exchange, McCarthy would commit to bringing certain specified bills to the floor for a vote—the list might include a clean debt-ceiling increase through 2017 (or even an abolition of the debt ceiling entirely), a continuing resolution funding the government at last year’s levels for the remainder of the fiscal year, something like the immigration bill that passed the Senate in 2013, and more. The details would have to be carefully negotiated (and other members of the leadership, perhaps starting with Rules Committee Chair Pete Sessions, would have to be brought on board), but there are no insurmountable practical considerations preventing such a deal.

Leaving aside whether such a deal would be good for the country, I don’t think it could actually be cut. Let’s say McCarthy has 210 Republican votes to be Speaker, and Pelosi says she will give him 15 more from her caucus. Don’t some of his 210 Republicans start defecting because they don’t want to be part of that kind of deal, or to be seen as part of it? Or think about budget votes. Is there a budget resolution that could win the votes of 200 Republicans and 30 Democrats? Or would you have to bust the budget caps to get those 30 Democrats, and end up losing some of those Republicans? Keep in mind that you can’t just keep substituting Democrats for Republicans by moving the deal left: At some point you’d end up with a governing majority–assuming you even cobbled together a majority–made up mostly of Democrats. A majority of the Republican conference can tolerate that on a piecemeal basis. (The partial government shutdown ended in 2013 when all House Democrats and a minority of House Republicans voted for a budget with no restrictions on Obamacare, for example.) But they’re not going to accept it as a general rule.

I am not at all sure that there is a stable equilibrium that includes a bipartisan majority of the whole House with a majority of Republicans inside it–and that’s what you’d need in this scenario. I’m sure Boehner et al often wished they could write off the 30 most demanding members of the Republican conference for all time and make up for them with Democrats, but I suspect that the main reason that path has never been pursued is that it wouldn’t actually lead anywhere.