by Dana Bash and Ted Barnett, CNN

Washington (CNN) – Washington (CNN) - A bipartisan amendment intended to increase Republican support for a Senate immigration bill would require 20,000 more border agents, completing a 700-mile fence on the frontier with Mexico and taking other steps before undocumented immigrants can get green cards, conservative Sen. Lindsey Graham said Thursday.

The proposal, negotiated by a group of senators from both parties known as the "Gang of Eight," also calls for deploying $3.2 billion in technology upgrades sought by the border patrol. Additionally, it seeks worker verification and border entry-exit controls before the 11 million immigrants living illegally in the United States can get full legal residency, according to the South Carolina Republican.

He noted it would take "a couple of years" to train and deploy the new agents in an expansion that would almost double the current force, and that the Department of Homeland Security would verify when the triggers for improved border security had been met to begin issuing green cards.

Graham, one of the four Republicans in the "Gang of Eight" that put together the compromise bill, also said the measure would include increased fees and other mechanisms to pay for the cost expected to exceed $20 billion.

Other GOP members of the "Gang of Eight" said they supported the plan.