It depends what one means by moral authority, which is one of the reasons I don't put a whole lot of stock in these rankings. Which isn't to say that Franklin Pierce isn't terrible. He is terrible on a damned near epic scale. If not for James Buchanan and Andrew Johnson, he would come in at the bottom of the pile on just about any set of rankings one could care about. For purposes of this post, I'm going to define moral authority as the ability to convincingly hold to one's convictions -whatever they are- and get others to abide by them.
For Pierce, the big issue here is slavery. He's more or less a standard Democrat of the era so not a lot else stands out. Pierce is a proslavery Democrat from New Hampshire, which isn't quite a standard alignment. The Antebellum Democracy is dominated by slaveholders and northern men willing to do their bidding, whom John Randolph coined the term doughface to describe. Not every northern Dem is one, but Pierce has a yeastier nose than most. Even doughfaces didn't get into reading antislavery Democrats of the party very often. Pierce did just that to John Hale over Hale's opposition to annexing Texas on antislavery grounds.
That's all in the 1840s, though. Come 1852, Hale runs against Pierce on the Free Soil ticket. He loses massively, what with the Free Soil party being a skeleton of its 1848 self and even then only a very junior third to the Democrats and Whigs. The Whigs will never contest another presidential election either, but no one knows that at the time. A big part of what kills them off is what happens with Pierce.
The Young Hickory of the Granite Hills comes into office on a relatively standard Democratic platform, notable in its embrace of territorial expansion. Pierce is looking at Cuba, which Spain doesn't want to sell, and probably some bites off Mexico. He manages to get the Gadsden Purchase and probably conspires with filibusters to seize Cuba by force. The idea is that a private military company headed by the former governor of Mississippi and backed by a Cuban exile community will land on the island, knock over the Spanish garrison, declare independence, and request annexation either immediately or within a year or two. His exact relationship to the filibusters is murky, but there's strong circumstantial evidence that someone in his administration gave them an official go-ahead and we have the instructions for the minister to Spain -we didn't send ambassadors back then- which refer to a policy of detaching Cuba from Spain with reference to purchase as a fallback option. All this new land was going to be for new slave states.
This is a fascinating, somewhat understudied element of the Pierce presidency because of the real problem. The two are tightly connected, though. After the Compromise of 1850, the political establishment of both parties were relieved at what they considered a near miss with civil war over the question of whether or not slavery would be permitted in the Mexican Cession. No one was happy, exactly, but the nation had passed through sectional battles before. The slave states won almost everything they wanted, as usual, and life went on. The watchword of the day was "finality." Because all the territory in the nation now fell one way or the other on slavery, there would be no need for further controversy.
So Pierce's foreign policy already throws that finality into doubt, though it would be harder to make a case for excluding slavery from lands where it already exists (Cuba) or which are adjacent to lands that either are or are almost certain to be enslaved (more of Mexico). But immediate adjacency is an issue within the United States as well.
The newly American Pacific Coast may as well be the far side of the world. The fastest way to get to California and all its gold is to take a ship down to Mexico, Nicaragua, or modern Panama, cross, and take a second ship. Mexico is an enemy, albeit a defeated one. Nicaragua is unstable and under pressure from the British. (There's a slavery connection in the worries about the British and Nicaragua too. They had a protectorate down there where they had settled some emancipated slaves from Jamaica.) Panama is farther away and so even more vulnerable to outside forces.
There's a lot of concern that without some secure way to connect it to the East, it cannot be held. Then James K. Polk would have started the Mexican War for nothing. That gives extra heft to the previous economic arguments in favor of building a railroad to the Pacific. Now it's a national security issue. It's also something that up and comers in Pierce's party have wanted to get done for a decade now. For a bunch of reasons, which also have a lot to do with slavery, any railroad that's going to get built needs to go from western Missouri to California. That means it must cross Indian Country, literally.
Indian Country is unorganized territory of the United States from which whites are barred, except for people passing through on emigrant trails, the military, and authorized agents. The idea is to leave it for the Indians to have forever, or until they do white America a solid and kindly die off. Or, you know, until white Americans change their minds. Since you can't engage in any economic activity at all in Indian Country unless you're an Indian agent, you can't just go build a railroad there. The stretch of Indian Country connecting Missouri to California needs to become a state, which first requires extinguishing Indian titles (usually by treaty) and freeing up land for whites to come in and take.
All of this is an old hat by Pierce's time. The process works like this:
Send people out to negotiate cessions from the Indians, usually in exchange for land still further west.
(often happening concurrently with the previous) Congress passes an organic act. This sets up a territorial government full of federal appointees, lays out boundaries, and names the place.
With a territorial government created (though not yet necessarily in place on the ground, it could take a while) whites can move in and start staking claims for preemption. Preemption is not homesteading, exactly, but it's close. Land would be sold at a fixed, low price to people who had taken at least formal possession of it.
The white population would grow. In short order (whenever the territorial governor felt it was time) they would elect a legislature and begin looking more like a state in all but name.
There are lots of rules of thumb for when the odometer turns over here, many of which were broken fairly often. The popular metric is meeting or beating the population of the least populous state, but there's no formal requirement at all. Basically whenever Congress wants, it can pass an enabling act that authorizes the territory to draw up a constitution and submit it for Congress' approval. If that's forthcoming, Congress admits the territory as a state. Somewhere in here its borders usually get trimmed too.
Simple enough, except that the land west of Missouri is land immediately west of Missouri's plantation belt and per the Missouri Compromise, that land has got to be free territory. So they'll have slave-stealing abolitionists inciting servile insurrection right next door. Diehard opposition from them keeps the land unorganized for quite a while, but a set of politicians who need an organic act badly for different reasons (Missouri's senator, his friends, Stephen Douglas of Illinois) can work around that problem. Missouri will not take a free neighbor, so the solution is to undo the Missouri Compromise.
Heads get put together about this in early 1854. Pierce and his Cabinet are firmly against any repeal, to the point where when word gets out that something like that is in the works their official newspaper attacks the idea. They know that voting slavery into a place that it was kept out of a generation before is explosive, but the backers of the Kansas-Nebraska Act (originally the Nebraska Act, but it becomes know by its more familiar title because of events I'll get to) insist. Douglas needs the act for his railroad and doesn't care either way about slavery. The Missouri senator, David Rice Atchison, cares about slavery and will see the land burn in hell before he allows a free territory. The Atchison-Douglas cabal get outflanked to the right by a pair of independent operators that pen them into an especially extreme form of repeal, which doesn't help.
The way things shake out, everyone needs a maximally proslavery organic act or it's not going to get done. A draft is hashed out over the weekend, at which point Pierce enters the story. They know Pierce is against this, but they know they need it. They're Democrats, like Pierce, and men Pierce needs to support his foreign adventures. On Sunday morning, they come to the White House. Pierce does not do business on Sundays for religious reasons, but the Nebraska Gang will not be deterred and they get Secretary of War Jefferson Davis to go up and bring him down.
Here's a moral test. Pierce is proslavery, functionally, but he has a firm commitment out in public against any Missouri Compromise repeal. He's also for the finality of the Compromise of 1850. He's a conservative, establishment guy who doesn't want to rock the boat. He has the power to veto this thing if it ever hits his desk. Given the chance to hold firm on his political convictions and keep with no more slavery controversies, Pierce caves.
By cave, I don't mean that he shrugs and lets it go. I mean when the group doesn't take yes for an answer and demands he agree in writing, then and there to sign off on, support, and make the Nebraska Act a test of party loyalty, he does it all. When the bill hits a firestorm of controversy in Congress, he applies the patronage screws hard to force reluctant Dems into line and make the thing law.