George Bailey did the best he could for as long as he could. But things eventually became too much for him. He had just misplaced a large amount of money and was all out of options. Sitting there at the bar, he prayed, not eloquently, but in earnest.
At the same time, all this friends and family were praying for him. All this prayerful supplication brought George to God's attention (represented by Gabriel).
This is a realistic portrayal of how prayer gets it done. A large amount of concerted prayer arouses power in the heavenly places.
Notice how the people of Bedford Falls pray. They seek God's help on behalf of a man they truly care about, who has spent his life looking after them.
Notice also how George Bailey prays. He says, "Dear Father in heaven, I'm not a praying man, but if you're up there and you can hear me ... [he starts crying] ... show me the way ... show me the way... " This is true prayer. The way George cries out to God for help must be sincere because, if God doesn't help him, then he doesn't know how else he's going to get help.
George's prayer here resembles Creed's song, "One Last Breath":
I'm holding to all I think is safe...
It seems I found the road to nowhere,
and I'm trying to escape.
I yelled back when I heard thunder
but I'm down to one last breath
and with it let me say,
let me say...
Hold me now
I'm six feet from the edge and I'm thinking
that maybe six feet
ain't so far down..."