Republicans can propose whatever they want to propose. No one is stopping them from authoring their own bill. And, of course, they can offer up whatever amendments they'd like to see implemented.
Typically, the opposition party puts together it's own bill and offers it up as an amendment in the nature of a substitute so that they can say "hey, we tried" after the amendment is rejected.
Instead of doing that, the Republicans have decided to just attack what the Democrats are doing. Now, that would be fine if the Republicans took the position that the status quo is fine but they aren't really doing that either. They're basically saying that there are problems and the Democratic solution sucks but they aren't offering a solution of their own.
Because they are saying they've been shut out of the debate on this particular one. I can see what their strategy is, can you?