It will. All corporations will see their debt servicing cost go up. A lot. They'll start the layoffs. How many posts on HN are about layoffs at this and that well-known tech company?
Once people fear for their job, they'll start being more cautious with their spending. Less demand means prices will go down.
At least that's how the Fed thinks. They are trying to destroy demand. They know they can't increase supply (obviously), so they are going after the demand. If 3.75% is not enough (spoiler alert, it won't be enough), they'll go to 4.5%. And then to 5%. If it's still not enough (spoiler alert, ... it won't be enough), they'll go higher.
You may not be convinced, and it looks like a lot of people are unconvinced, but the Fed means business. All the members of the Fed know history, and know that in the '70s the Fed lacked the backbone to keep the rates high enough long enough to beat the inflation. They were trying to have both low inflation and some semblance of growth. They got neither. Stagflation for a whole decade.
People who forget history repeat it. Powell will not let history repeat on his watch.