Last week, I wrote this about the Supreme Court's vacancy:

assuming Kennedy swings the same way, decisions that would've swung liberal will still swing liberal. decisions that would've swing conservative will go back to the lower court; but that is not necessarily a conservative victory - that depends on what the lower court said in the first place. sometimes conservatives challenge lower court rulings, after all.

and, since conservatives have one fewer solid vote, the likelihood of conservative-friendly cases even being accepted to be heard is reduced (takes 4 votes to hear a case)

Today,
TPM wrote this:

The Supreme Court has only been in session without Justice Antonin Scalia for a week. But already, his death is affecting cases, and particularly decisions not to take certain cases to the Supreme Court without the guarantee of his vote. Last week, Dow Chemical made headlines by opting for a $835 million settlement in a class action lawsuit rather than risk having the case heard by a Scalia-less Supreme Court. A lower court had already ruled against the company for allegedly conspiring to fix prices for industrial chemicals, and prior to the settlement, Dow had appealed to the Supreme Court to overturn the ruling.

...

But it's not just corporate interests that are quickly recalibrating their legal strategy with the loss of Scalia. A guns right groups decided to forgo a Supreme Court petition last week because the court had lost its conservative tilt.

What the GOP is fighting against is having a 5-3-1 situation in favor of liberal judges, instead of the 4-4-1 situation that existed before Scalia died. But a 4-3-1 situation in favor of liberals isn't such a great place for the GOP to be, either.

Not that this excuses the GOP's latest tantrum.