Traditionally, juries have been required to reach a unanimous decision. A few states do allow non-unanimous convictions (such as by a 10-2 vote), but they’re in the minority. So what happens when a jury can’t reach a decision?
If a jury is well and truly stuck, the judge will declare a mistrial. The prosecutor has the option of bringing charges again (double jeopardy doesn’t prevent this), but of course that will involve lots of extra time and money for the government. Plus the accused and any witnesses will have to go through another trial. Judges really, really don’t want this to happen.
If the jury is hung, about half the states allow something called an Allen charge. Allen charges are allowed in federal cases as well. Named after an 1896 murder case, an Allen charge is essentially a plea from the judge to the minority members of the jury, urging them to consider joining with the majority. The charge emphasizes the potential costs of a retrial, and it points out that the evidence was strong enough to convince most of the jurors. It’s worded strongly enough that it’s often called a “dynamite charge.”
The Allen charge is controversial. Many argue that it’s coercive. For that reason and others, about half the states forbid it. In those states, if a jury is deadlocked, a judge may ask them to consider further. But if that gets them nowhere, a mistrial will be declared.