Business groups such as the U.S. Chamber of Commerce have remained neutral on the issue.
Sens. Rob Portman, R-Ohio, and Pat Toomey, R-Pa., were crafting amendments to the bill dealing with religious exemptions.
Seven Republicans and 54 Democrats stood together Monday and cleared the bill past its first hurdle on a 61-30 vote, setting the stage for possible passage by week's end. The Employment Non-Discrimination Act would prohibit workplace discrimination against gay, bisexual and transgender Americans.
The legislation, the first significant gay rights bill since Congress ended the ban on gays serving openly in the military in 2010, faces strong opposition in the House, with Boehner rejecting the measure.
Final passage would cap a 17-year quest to secure Senate support for a similar discrimination measure that failed by one vote in 1996, the same year Congress passed and President Bill Clinton signed the Defense of Marriage Act, the law prohibiting federal recognition of same-sex marriage.