The “Gang of Eight” immigration reform bill could be up for a vote before the full Senate by the first week of June, Majority Leader Harry Reid said Thursday.

Reid, D-Nev., vowed in a floor speech to take up the legislation, “as soon as it is ready,” even if it means interrupting work on other bills, including debate on an important farm bill set to begin soon.

A Senate aide point out that the Judiciary panel is expected to finish amending the immigration reform bill before the week-long Memorial Day recess begins on May 27, so the measure should be ready for floor debate as soon as lawmakers return from the recess on June 3.

The bill combines improved border security with immediate legalization and a pathway to citizenship for most of the nation’s 11.5 million illegal immigrants. It also increases visas for workers who are high and low skilled and it creates a guest worker program for farm workers.

The bill is now under debate in the Judiciary Committee, where Republicans are attempting to strengthen its border security provisions.