Republicans are asking for something they have already: a bill that can pass both houses.

[Mass]

Just put it on the floor.

http://www.washingtonpost.com/blogs/post-partisan/wp/2013/10/09/postscript-cantor-and-the-need-for-negotiation/

and boblesch’s:
Sorry you forgot about it, Eric – let me remind you. Boehner admitted on Sunday he made a deal with Reid in July. The CR to fund the government at sequester levels was the result. The Senate passed the bill. The House will pass the bill as soon as it is allowed on the House floor for a vote. The bipartisan deal was done 4 months ago!

Aha. So if Cantor just wants to hash out a deal with the Democrats that could pass the House, according to several news agencies’ vote counts and members of the House GOP, he’s already got one. The “clean” continuing resolution (to fund the government and stop the shutdown) would get an estimated 219 votes. The bill could pass the House, just not the House leadership. As Cantor argued, America elected the House. Which would pass the bill. But America did not elect the House leadership, which prevents the House from passing the bill.