Yes. Well, sort of. Starting with Thomas Jefferson, the State of the Union Address was delivered as a written "Message To Congress" and this tradition continued until Woodrow Wilson ended it, and reverted back to giving the address in person like George Washington and John Adams had. So maybe not "said" but certainly "wrote".
In Franklin Pierce's fourth and final Message To Congress, delivered on December 2, 1856, he talked about the growing disunion movement, which he attributed to radicals on both sides (Pierce was very much a "blame both sides" type of politician):
...[H]ostile [state] governments, driven at once and inevitably into mutual devastation and fratricidal carnage, [are] transforming the now peaceful and felicitous brotherhood into a vast permanent camp of armed men like the rival monarchies of Europe and Asia...[T]hey endeavor to prepare the people of the United States for civil war by doing everything in their power to deprive the Constitution and the laws of moral authority and to undermine the fabric of the Union by appeals to passion and sectional prejudice, by indoctrinating its people with reciprocal hatred, and by educating them to stand face to face as enemies, rather than shoulder to shoulder as friends.
But he did give them the benefit of the doubt, saying that while these radicals truly meant well and were not consciously trying to divide the Union, that was certainly the result, and the American people have rejected calls for disunion and needed to continue to do so:
"[I]n the progress of events we had reached that consummation, which the voice of the people has now so pointedly rebuked, of the attempt of a portion of the States, by a sectional organization and movement, to usurp the control of the Government of the United States.
"I confidently believe that the great body of those who inconsiderately took this fatal step are sincerely attached to the Constitution and the Union. They would upon deliberation shrink with unaffected horror from any conscious act of disunion or civil war. But they have entered into a path which leads nowhere unless it be to civil war and disunion, and which has no other possible outlet."
James Buchanan's fourth and "final" Annual Message To Congress on December 3, 1860, was even more dire. This was still before any of the Confederate states had seceded, but after some of them, like South Carolina and Mississippi, had already passed legislation approving public votes to hold secession conventions, which would begin later in December.
He didn't say directly that the Union was in bad shape, but posed it as a question, and what could be done to solve it:
"Why is it, then, that discontent now so extensively prevails, and the Union of the States, which is the source of all these blessings, is threatened with destruction?"
After detailing his own views on why compromise was imperative over the contentious slavery issues of the time, he wrote that peace was still possible. War was not the answer, and as bad as it would be, disunion of the Union was ultimately a better alternative than war:
"The fact is that our Union rests upon public opinion, and can never be cemented by the blood of its citizens shed in civil war. If it can not live in the affections of the people, it must one day perish. Congress possesses many means of preserving it by conciliation, but the sword was not placed in their hand to preserve it by force.
But just a month after giving this speech, he gave another Message To Congress, on January 8, 1861. By this time, South Carolina had seceded, Mississippi and several other states were holding secession conventions and were just days away from seceding, and multiple members of his Cabinet had resigned over the unfolding Secession Crisis and his handling of it.
The Fort Sumter crisis was causing big headaches, and there were public demonstrations against the United States in many cities in the South (mostly in the Deep South), with efforts underway to convene further secession conventions. At the same time, in Philadelphia and other Northern cities, there had been pro-Union demonstrations condemning South Carolina's actions.
South Carolina had also passed a resolution to raise 10,000 militia troops, while Georgia (not yet seceded but having convened their secession convention) had already provisioned $1 million to fund their state military operations. In addition to Fort Sumter, many U.S. Army and federal military installations had been raided where they weren't well-guarded.
So in Buchanan's final final Message To Congress, he basically said that the State of the Union is very bad, condemning "the dangers which threaten...the existence of the Union", and calling the situation already "a great calamity" at the time of his previous speech that had just gotten worse since:
"I deeply regret that I am not able to give you any information upon the state of the Union which is more satisfactory than what I was then obliged to communicate. On the contrary, matters are still worse at present than they then were. When Congress met, a strong hope pervaded the whole public mind that some amicable adjustment of the subject would speedily be made by the representatives of the States and of the people, which might restore peace between the conflicting sections of the country. That hope has been diminished by every hour of delay; and as the prospect of a bloodless settlement fades away, the public distress becomes more and more aggravated...
"The Union is a sacred trust left by our revolutionary fathers to their descendants; and never did any other people inherit so rich a legacy...Should the Union perish in the midst of the present excitement, we have already had a sad foretaste of the universal suffering which would result from its destruction. The calamity would be severe in every portion of the Union, and would be quite as great, to say the least, in the Southern as in the Northern States."
He ends by saying that he hopes the people in the country, and in Congress, will pause long enough to reflect and reconsider the present calls for disunion:
"Time is a great conservative power. Let us pause at this momentous point and afford the people, both North and South, an opportunity for reflection. Would that South Carolina had been convinced of this truth before her precipitate action! I, therefore, appeal through you to the people of this country to declare in their might that the Union must and shall be preserved by all constitutional means. I most earnestly recommend that you devote yourselves exclusively to the question how this can be accomplished in peace. All other questions, when compared with this, sink into insignificance. The present is no time for palliatives; action, prompt action, is required. A delay in Congress to prescribe or to recommend a distinct and practical proposition for conciliation may drive us to a point from which it will be almost impossible to recede."
So, while it might seem a bit silly in this day and age, the State of the Union has not always been strong, and for much of the 19th Century, it was very much in danger of collapsing. At the lowest points, Presidents Pierce and Buchanan certainly pointed this out.
EDIT: Thanks for the silver!
While not in his State of the Union address, it is worth noting that President Jimmy Carter did make a fairly brutally honest address in his famous ‘Crisis of Confidence’ speech in July 1979. In a televised address to the American public, Carter described the problems faced by the US as largely a society lacking self-belief:
"[i]t's clear that the true problems of our Nation are much deeper—deeper than gasoline lines or energy shortages, deeper even than inflation or recession. … The threat is nearly invisible in ordinary ways. It is a crisis of confidence. It is a crisis that strikes at the very heart and soul and spirit of our national will. We can see this crisis in the growing doubt about the meaning of our own lives and in the loss of a unity of purpose for our Nation.”^1
Carter’s address was unprecedented in its critical analysis of the US; a president had not previously addressed the American public in such pessimistic terms about its future. As Sean Wilentz put it,
'[i]t was a form of anti-politics unlike any Americans had ever seen – the chief magistrate, who was supposed to inspire the nation and lift it out of its slough of despond, was instead complaining about unrelieved anguish and emptiness.'^2
Even in the darkest days of the Great Depression, President Roosevelt had famously promised the American people that "the only thing we have to fear is fear itself – nameless, unreasoning, unjustified terror which paralyzes needed efforts to convert retreat into advance."^3
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