One day after seeming to agree to an acceptable compromise on Gov. Cuomo’s proposed 2 percent cap on property-tax levies, Assembly Speaker Sheldon Silver yesterday seemed to be sticking a poison pill in the fine print.

If Silver insists on a hard expiration date for the cap, the governor will need to start again.

Silver and his allies in the state’s teachers union were always seen as the chief obstacle to passage of the most popular initiative of the highly popular new governor. But hope resided in the coming expiration of New York City’s seemingly perpetual but legally temporary rent regulations, last renewed in 2004.

The two issues — a cap on property taxes outside New York City, and price controls applying mainly to apartments within the city — obviously are unrelated. But since the renewal of rent control is a top Silver priority, it seemed likely all year that their fates would be linked in the end.

Sure enough, with the clock ticking on an as-yet unfinished rent-regulation deal, the speaker on Tuesday introduced his own tax-cap bill — matching Cuomo’s priorities in almost every significant respect.

Cuomo has been insisting all along on a broad, tight and permanent cap — like the one passed by the GOP-controlled Senate in January. And the speaker’s changes to the governor’s basic tax-cap structure are relatively minor.

The most significant change is a partial exclusion of pension costs from the 2 percent cap. But the exclusion is a carefully limited one, effectively raising the cap by an average of 1 to 1.5 percentage points (depending on how high pension costs spike in the next few years). What remains would still be among the tightest property-tax limits in the country.

Silver isn’t proposing the permanent tax-cap law sought by Cuomo, but the final provision of the bill he introduced amounts to the next best thing. The tax cap, it stipulates, shall remain in effect as long as New York continues to regulate rents. Of course, as far as Assembly Democrats from the city are concerned, the “temporary” rent law will never expire.

So we were treated to one of Albany’s Kumbaya moments — a Capitol press conference where the governor joined with the legislative leaders to declare that a deal had been reached on his top legislative priority.

Within 24 hours, however, Silver seemed to be shifting gears. “When you see the bill actually, the actual final bill, the contemplation is it will have a specific date in it,” he told The Post’s Albany bureau chief, Fred Dicker. “The date will correspond to the date that rent regulations expires.”

Huh? That’s a big difference. Under Silver’s bill as introduced, a tax-cap law could be repealed or modified in the future only by agreement of both houses of the Legislature — or by one house alone, but only if it is also willing to kill rent control (which, while desirable, is highly unlikely).

By contrast, a tax cap with its own specific expiration date could be killed through inaction of only one house of the Legislature.

While Senate Majority Leader Dean Skelos joined in celebrating this week’s agreement, his position on the sunset issue is unclear.

In short, while the announced tax-cap deal is worth celebrating, don’t pop the cork yet.