Rather, they would have used a word like "charity", or "for charitable contributions", or "for the poor". The term "general welfare" already applies to things that the feds were already empowered to do.
Also consider, that if we take a loose flexible interpretation of "general welfare", and if we consider that later Amendments over rule earlier ones where they are in conflict, then congress could claim it empowers them to do just about anything, as long as they feel it is for the "general welfare".
For instance, they could pass a law against the Christian bible because it upsets gay people. For the general welfare you understand. The first amendment swept aside, because it is conflict with "general welfare"...
In magnitude, the crisis created by the great depression ranks number 2 behind the Civil War. It looked to farmers who lost their livelihood and homes and to the masses of unemployed like capitalism was a failure. There was looting, homelessness, riots, strikes, and a high interest in alternatives to our system of government, namely, Communism.
Shanty towns called Hoovervilles, after the president that basically did nothing aside from promise that prosperity was just around the corner, sprung up around the country (one in Oklahoma is said to have stretched for 10 miles). The old means of dispensing "charity" were overwhelmed.
They used to tell me I was building a dream
And so I followed the mob.
When there was earth to plow or guns to bear,
I was always there, right on the job.
They used to tell me I was building a dream
With peace and glory ahead --
Why should I be standing in line, just waiting for bread?
Once in khaki suits, gee, we looked swell
Full of that Yankee Doodle-de-dum.
Half a million boots went slogging through hell,
And I was the kid with the drum.
Say, don't you remember they called me Al,
It was Al all the time.
Why don't you remember, I'm your pal --
Say, buddy, can you spare a dime?
Summed up in the song, Brother, Can You Spare a Dime is the confusion, and frustration of men who had been hard working and productive, who had served our country and found themselves out of work, out of luck, reduced to begging.
Now, I suppose you can argue that a more Constitutional approach to insuring the general welfare, would be the use of police and military force to restore order, and indeed, that was done on more than one occasion; or, as FDR did, push through legislation to restore order by restoring hope.
Was an economic crisis of this magnitude foreseen by the founding fathers? How would they have responded had it occurred on their watch? IMHO, they would have debated, and acted to preserve our Republic and capitalism to the best of their abilities with respect for their fellow citizens.