The conventional wisdom on how New York legislators will redraw their congressional maps went out the window Tuesday night, with Democrat Kathy Hochul stealing a Republican-leaning western New York district in a special election.

The Empire State’s congressional delegation has to shrink by two members due to growth that lagged the national average over the last decade.

Control of redistricting is split between the two parties. Under that arrangement, both parties are likely to lose one seat, and the thinking had long been that one upstate Republican and one New York City-area Democrat would be left without seats when the game of musical chairs ended.

But Hochul’s win throws a sizeable wrench into that premise. And by Wednesday morning, her win was forcing consultants and incumbents all over the state to re-evaluate their expectations about the congressional redistricting process.

“It screws it up majorly,” said one Democratic strategist familiar with the redistricting process.

Here’s the problem Hochul’s win creates:

The 26th district that she won sits in precisely the part of the state where a district is going to have to be cut. And the least-tenured members — aka Hochul -- are generally the odd men (or women) out when it comes to redistricting. By those measures, she’s an obvious target for elimination.

But given that the upstate area is really the only area where a Republican district can be eliminated — and that Hochul’s district has more population than all of its neighbors — it’s not quite so simple to take her out.

In fact, there doesn’t seem to be one good way to draw Hochul out of a district.

Some strategists are floating the idea of cutting two upstate districts rather than one upstate and one downstate. But as the Cook Report’s David Wasserman notes, this is nearly impossible, given that the populations in upstate and downstate are almost ideal for cutting one seat from each.

Some suggest that the maps could eliminate an upstate Democrat and a downstate Republican rather than the other way around. But there are just two Republicans downstate — Reps. Pete King and Mike Grimm — and neither is easy to cut. King carries significant clout in the state and is unlikely to see his Long Island-area district messed with, and Grimm represents a district that is 75 percent on Staten Island.

In short, about the only way that Hochul will be drawn out of a district is if Democrats lose both seats in the redistricting fight, or if the two sides reach some kind of agreement under which Hochul and a neighboring Republican like freshman Rep. Tom Reed get drawn into the same district. Even then, though, Democrats would risk losing two seats, and given their historical dominance in the state, that’s unlikely to be an acceptable outcome.

At the same time, though, leaving Hochul as-is is hardly ideal for Democrats either. She holds a conservative-minded seat and would likely need some redistricting help to shore herself up in future elections. And that help may be hard to come by.

Thirteen-term Rep. Louise Slaughter (D-N.Y.) has plenty of Democratic voters to spare in her 28th district, which spans Buffalo and Rochester and went 69 percent for President Obama in 2008. But her district needs to add more population than any other district in the state, and her seniority means it will be harder to change her district significantly.

The other nearby Democrat, Rep. Brian Higgins (D-N.Y.), also needs to add a signfiicant amount of population, making it very difficult to cut into his district in the western corner of the state.

“In light of yesterday’s results, if you’re Louise Slaughter, you’re more nervous today than you were yesterday,” said New York GOP consultant Mike McKeon. “I don’t think they’re going to be able to save both (Slaughter and Hochul).”

Democrats disagree. Democratic redistricting guru Mark Gersh said Hochul could get some help by taking more Democratic areas of Reed’s territory — in the Rochester area, for example — while Reed’s district shifts to the east. Hochul wouldn’t be completely safe, but she would be safer.

The most likely targets for the two cuts, according to those familiar with the state’s redistricting process, are Democratic Reps. Gary Ackerman and Carolyn McCarthy downstate and any of the five upstate freshman Republicans.

That may still be the case after Hochul’s win Tuesday, but getting to that outcome just became significantly more difficult.

They’ve got plenty of time, though, with the state unlikely to take up its new congressional map until next year. In the meantime, there will be plenty of hand-wringing.