Saying the Putnam is a next step from AMC12 problems is like saying the NBA is a next step from pickup basketball with friends in middle school! There are people who can do Putnam problems for fun, but those people generally know who they are already.
Solving problems 1-4 on each day of the Putnam with an "unlimited" amount of time is not a ridiculous expectation. Putnam's difficulty is partly due to its time format.
Putnam problems are not considerably harder than AIME problems, and AIME is definitely the next step from AMC12. Anybody who can solve a few AIME problems can certainly solve A1 on the Putnam of almost every year.
