If you believe in broadening the franchise in democracy for the many rather than the few, the complaints from people who spent a chunk of their weekend waiting at the polls are infuriating. Like this one from Myrna Peralta in The Miami Herald: “This is America, not a third-world country. They should have been prepared.”

She spent almost two hours in line with her 4-year-old grandson before being shut out in Doral, the home of the election headquarters in ever-crucial Miami-Dade County. This was on Sunday, after elections officials opened the doors for four hours for in-person absentee voting — and then suddenly shut them midstream when Miami-Dade Mayor Carlos Gimenez demanded it. (He said he hadn’t agreed to the Sunday hours.) Almost 200 people were waiting and some of them actually banged on the doors, shouting “Let us vote!”

Eventually, amid a barrage of phone calls to his office, the mayor gave in. Everyone who was still in line at 5 p.m. — about 400 people — got to cast ballots. But who knows how many gave up along the way. And why all the waiting and the craziness in the first place?

The problem is that early voting has become intensely partisan. Democrats increasingly press for more of it and Republicans for less. It’s sad: In a country known for low voting rates, where Election Day isn’t a holiday and Tuesday lines at the polls deter people from showing up, early voting should be a bipartisan cause. Both parties could put their energy into increasing turnout for their side. Instead, the Republicans who litigate against early voting — and in favor of voter ID — talk about following the rules, even though the rules they are crafting have such self-serving ends, and inveigh against voter fraud, even though in-person vote stealing almost never actually occurs.

In Miami-Dade, the weekend chaos was the result of the Republican mayor’s response to litigation over a state law that stopped early voting on the Sunday before the election. That’s right: There used to be more opportunities to vote in Florida and now there are fewer.

Democrats went to court over the weekend over extending early voting in Broward and Palm Beach counties as well as Miami-Dade. (Does anyone else feel like just listing the names of these counties brings on a Bush vs. Gore migraine?) The Democrats went to court after Gov. Rick Scott, a Republican, refused to extend early voting despite all the complaints about long lines and voters who were giving up and leaving. Scott claimed that “the process was running smoothly,” The New York Times reported. He’s also the guy who pushed through the state law cutting back early voting from 14 days to eight, as well as eliminating it altogether this past Sunday. (The polls only ended up open on Sunday in some places because of the lines and snafus on Saturday.)

Republicans also insisted in cutting back on early voting in all-important Ohio, where it was allowed for each of the five weekends before Election Day four years ago, and this year is allowed for only one.

It’s hard not to draw a line between that narrowing and a study released last month by the Lawyers’ Committee for Civil Rights Under Law, which found that black voters vote early at 26 times the rate of white voters. This study was conducted in Cuyahoga County, an Obama stronghold.

Then there’s this statement in The Washington Post from the Ohio AFL-CIO, which is campaigning hard for the president: “This is what works for working-class folks. If they have a 9-to-5 job, they’ve got kids to pick up and a lot going on, the weekend is when they’ll be able to get time to go vote.”

I suppose you could argue that given the resistance from Republicans, it’s amazing that early voting happens at all in swing states. The federal appeals court that forced Ohio to open the polls for this past weekend pointed to “the unacceptably burdensome situation at many Ohio polling sites during the 2004 election where, in some countries, voters were required to stand in line for long hours and until late at night.”

The lesson of the weekend from Florida is that cut off by officials like the Miami-Dade mayor, early voting can also leave voters hanging. Maybe the hope is that if you frustrate people enough, they’ll quit asking for it. But what we should want is exactly the opposite: More polling places open at more times when all kinds of people can get to them. And a commitment from both parties to fight the turnout war instead of this misguided fight to choke off access.