Political Scientist Chris Lawrence makes an astute point in the comments of a Doug Mataconis post: the way things were heating up in Florida, the case would have ended up before the United States Supreme Court, one way or another.
One other thing to bear in mind: as of the date of the court’s decision, the Florida state legislature was in the process of moving a bill to award all of the state’s electors to Bush (which under the 12th Amendment was its right; Scalia is often mocked on the left for saying in Bush v. Gore there is no right for the people to elect the president, but it’s right there in the text of the Constitution). Inevitably that would have been challenged in court. And inevitably that case would have ended up on the U.S. Supreme Court’s docket, because I can’t imagine the equally-politicized Florida Supremes ruling for the legislature’s position. So denying cert here just would have delayed matters further.
The original sin, in my view, was Gore's attempt to recount just the votes in a few heavily Democratic counties. I'm not saying that Bush would have done any different, had the positions been reversed. But once that had happened--and Democrats on local election boards and the Florida Supreme Court had decided to go along--there was no longer even a pretense that this was about anything other than naked post-facto power grabs, using whatever political levers your party controlled. "Count all the votes", which most progressives now remember as the rallying cry, actually came very late in the process, and only after the Supreme Court of the United States told the Florida Supreme Court that no, it couldn't just let Al Gore add in some new votes from Democratic Counties his team had personally selected.
By the time Bush v. Gore petitioned for cert, both sides were more or less nakedly maneuvering to declare their candidate the winner. The Florida Supreme Court's November 21st decision was outrageous and completely unjustifiable. So was Katherine Harris's clear determination to stop any recount that might help Gore. And while the Florida legislature was arguably within its constitutional rights to intervene to declare Bush the winner, this contravened more than a century of custom . . . and the behavior of the state Republican Party in the weeks prior made this seem less like a bid for fairness and closure than a bid to make their guy president. The Florida Supreme Court would undoubtedly have ruled against the legislature, but of course, their prior behavior made it impossible to claim that they were just trying to insure a fair and democratic process.
Had the Court let Bush v. Gore go, it would have ended up back there in a few weeks anyway--but this time, as a full-blown constitutional crisis.
So I agree with Lawrence: it's hard to see how, in the end, the Supreme Court could have stayed out of it. The process was hopelessly tainted, and the questionable tactics were escalating. Some neutral party had to step in, and the Supreme Court was the closest thing we had. Unfortunately, they didn't have any neutral choices. By December 11th, they were faced with the option of choosing which side's shenanigans to ratify. Given that, they probably came up with the least problematic response: you can't possibly complete a full recount in time, so stop.