Strange but true.

By taking the lead to pass a budget that includes an income-tax increase, Illinois Democratic lawmakers rescued state government and those who rely on it, at least for now. But, in the process, they lost their best issue to stop Gov. Bruce Rauner’s re-election in 2018.

In contrast, Rauner proved he was willing to drive the state off the cliff to make his point and, as a result, got the campaign issue he believes will give him another four years to break Democratic power in the state.

Funny how these things work.

Everything that happened this past week in Springfield was done with a wary eye toward next year’s elections, which makes this a good time to reassess where we stand.

Rauner, facing low voter approval ratings after more than two ineffectual years pushing his vision of “reform,” emerges from the budget passage over his vetoes no worse off than before, arguably better.

As I was trying to say the other day, Rauner loves this income-tax increase as much as he loves to hate on it.

Not only does it remove the No. 1 symbol of his failings as governor — the inability to pass a budget — but he now also can claim the tax increase that’s necessary to pay for it was all the work of the villain he has created for this very purpose: House Speaker Michael Madigan.

OPINION

Even as I type those words, another batch of angry readers are reaching for their computers to reassert Madigan’s arch-villainy, oblivious to the fact that tens of millions of dollars have been spent to condition them to believe exactly what they now absolutely know to be true — that this one man is at the root of all their frustrations with government.

Tens of millions more dollars now will be spent to convince them this was “Madigan’s tax increase” and that whichever Democrat he supports to replace Rauner must be presumed to be his pawn, so great and powerful is the speaker’s dark wizardry.

Look, it’s easier to defend an income-tax increase than it is to defend Madigan. He even looks the part of the villain.

But all the television commercials, newspaper editorials and mock-umentaries in the world don’t change the fact that he and his members stepped up — with the help of 15 House Republicans — to take the first necessary step to keep the state afloat, while Rauner was willing to watch it sink.

Income-tax increases aren’t popular, and there likely will be a political price to pay.

Coming on top of a recent series of property-tax increases and coupled with nonstop advertising aimed at overturning Cook County’s sweetened beverage tax, we might even have the makings of a tax revolt.

Some of that anger will be directed at House Democrats in hopes of overturning the majority that gives Madigan his leadership role.

Mostly on a lark, I wrote in January about the possibility that, in the process of fighting each other, Rauner and Madigan might both end up losing. Some tell me that’s not really so farfetched.

One concern for me is then we’d have to deal with all those Republican notions we have been able to ignore in Illinois, such as making sure people use the bathroom “that God intended.”

Meanwhile, the Democratic candidates who are vying to replace Rauner had trouble getting traction from the budget agreement.

None of them took issue with the income-tax increase. In fact, the major candidates all want Illinois to enact a progressive income tax to extract even more money from the state’s wealthiest residents.

That’s the right answer, but it just became a more difficult case to make.