What does "hard pushed in argument" mean in this context?
In "In the Midst of Alarms" (1894) by <PERSON>, a blacksmith, <PERSON>, did an embarrassing trick to break the conceit of his New Yorker client in front of the crowd in his smithy, but he failed
<PERSON> saw there was no triumph over him among his crowd, for they all evidently felt as much involved in the failure of <PERSON>’s trick as he did himself; but he was sure that in future some man, hard pushed in argument, would fling the New Yorker at him. In the crisis he showed the instinct of a <PERSON>.
“Well, boys,” he cried, “fun’s fun, but I’ve got to work. I have to earn my living, anyhow.”
<PERSON> enjoyed his victory; they wouldn’t try “getting at” him again, he said to himself.
<PERSON> strode to the forge and took out the bar of white-hot iron. He gave a scarcely perceptible nod to <PERSON>, who, ever ready with tobacco juice, spat with great directness on the top of the anvil. <PERSON> placed the hot iron on the spot, and quickly smote it a stalwart blow with the heavy hammer. The result was appalling. An instantaneous spreading fan of apparently molten iron lit up the place as if it were a flash of lightning. There was a crash like the bursting of a cannon. The shop was filled for a moment with a shower of brilliant sparks, that flew like meteors to every corner of the place. 624
Everyone was prepared for the explosion except <PERSON>. He sprang back with a cry, tripped, and, without having time to get the use of his hands to ease his fall, tumbled and rolled to the horses’ heels. The animals, frightened by the report, stamped around; and <PERSON> had to hustle on his hands and knees to safer quarters, exhibiting more celerity than dignity. The blacksmith never smiled, but everyone else roared. The reputation of the country was safe. <PERSON> doubled himself up in his boisterous mirth.
“There’s no one like the old man!” he shouted. “Oh, lordy! lordy! He’s all wool, and a yard wide.”
<PERSON> picked himself up and dusted himself off, laughing with the rest of them.
“If I ever knew that trick before, I had forgotten it. That’s one on me, as this youth in spasms said a moment ago. <PERSON>, shake! I’ll treat the crowd, if there’s a place handy.”
1- I found that "hard pushed" means "face a great difficulty in doing something", but I can't get the whole meaning of this phrase in this context.
2- What did he exactly mean by "I’ll treat the crowd, if there’s a place handy".
Thanks in advance. 417