First off, State of the Unions were only given as speeches from Woodrow Wilson on. Prior to that, they were written messages from the President sent to Congress. I'm unsure whether that distinction matters too much to you.

Secondly, to answer your question, the most pessimistic State of the Union in terms of its answer to that key question is Gerald Ford's in 1975.

http://www.presidency.ucsb.edu/ws/?pid=4938

The whole speech is here, but here's the key section you're interested in.

Today, that freshman Member from Michigan stands where Mr. Truman stood, and I must say to you that the state of the Union is not good: Millions of Americans are out of work. Recession and inflation are eroding the money of millions more. Prices are too high, and sales are too slow.

This year's Federal deficit will be about $30 billion; next year's probably $45 billion. The national debt will rise to over $500 billion. Our plant capacity and productivity are not increasing fast enough. We depend on others for essential energy.

Some people question their Government's ability to make hard decisions and stick with them; they expect Washington politics as usual. Yet, what President Truman said on January 5, 1949, is even more true in 1975. We are better able to meet our people's needs. All Americans do have a fairer chance to pursue happiness. Not only are we still the foremost nation in the pursuit of peace but today's prospects of attaining it are infinitely brighter.

There were 59 million Americans employed at the start of 1949; now there are more than 85 million Americans who have jobs. In comparable dollars, the average income of the American family has doubled during the past 26 years.

Now, I want to speak very bluntly. I've got bad news, and I don't expect much, if any, applause. The American people want action, and it will take both the Congress and the President to give them what they want. Progress and solutions can be achieved, and they will be achieved.

My message today is not intended to address all of the complex needs of America. I will send separate messages making specific recommendations for domestic legislation, such as the extension of general revenue sharing and the Voting Rights Act.

The moment has come to move in a new direction. We can do this by fashioning a new partnership between the Congress on the one hand, the White House on the other, and the people we both represent.

Ford's message, coming in the immediate aftermath of a President chased from office, at a time following the 1973 oil shock when gasoline was scarce and expensive, when inflation rising and the economy was stagnating, when unemployment was rising and the nation's mood was listless, cynical, and depressed, is the most somber State of the Union I was able to find. Even Roosevelt's during World War II aren't as bleak as that above passage.