Probably, but putting an offer that included elimination of Obamacare, Corporation for Public Broadcasting and any two other agencies, would have been a counter offer showing just how insulting Obama's offer was. Besides, if they can force Obama to make a concession for keeping those things they are ahead. Also the house should tell Obama that if they go over the cliff, the deal gets worse for him, an additional agency will be added for every month.
Obama already has made it clear he won't cut PBS and Obamacare. No one expects differently. There would be no "ahead" in this proposal.