WASHINGTON — A measure that would outlaw workplace discrimination based on sexual orientation and gender identity overcame a significant obstacle in the Senate on Monday as seven Republicans crossed party lines and voted to begin debate on the bill.

The 61-30 vote marks the first time since 1996 that the full Senate will consider a measure to extend federal nondiscrimination law to gay, lesbian and bisexual people — a stark reminder, supporters said, that as the public has come around to accepting gay rights, Congress has been slow to keep pace.

It is also the first time that either house of Congress has voted on a nondiscrimination bill that includes transgender people.

Before the vote, supporters spoke of making history. The occasion moved Senator Mark S. Kirk, Republican of Illinois, to make his first speech in the Senate since suffering a stroke last year. None of the Republicans voting against the measure spoke up.