There is a House bill (in fact, there have been several, IIRC), but it will have no clout without Senate support. They are not withholding funding (because they can’t); they are saying that if it is funded, they will not allow the rest of the government to go ahead.
This is a very positive thing, because as long as Harry Reid is in charge and the Dems have a majority, they’re not going to be able to actually repeal the thing.