"Discrimination is wrong," Hatch said. "The bill exempts churches and religious organizations, and the bill prohibits quotas and preferential treatment."
Sen. Mike Lee, R-Utah, like most Republicans, opposed the measure, saying it could have unintended consequences and is too subjective when it comes to determining when an employer is liable.
His criticism didn't stop there.
"It doesn't account for likely negative effects on our economy and, though there has been some attempt to mitigate a clear violation of Americans' religious liberty, the bill still does not effectively protect conscience rights," he said in a statement.
Hatch promised to work with his Republican colleagues on potential amendments that would strengthen religious-liberty protections.
His stance, and that taken by Heller, tracks that of their shared faith, which has spent heavily in states to oppose gay marriage but has recently taken a softer position when it comes to other gay-rights issues.
The Church of Jesus Christ of Latter-day Saints supported a nondiscrimination in employment and housing ordinance approved by the Salt Lake City Council in 2009 and has negotiated with gay-rights leaders on a potential state law in Utah in recent years.
The faith hasn't taken a position on the federal law.
Two Mormon Democrats in the Senate Majority Leader Harry Reid of Nevada and Tom Udall of New Mexico support the nondiscrimination law and gay marriage.
Heller noted that Nevada already has a state law banning employers from disciplining or firing workers for their sexual orientation. Utah is among 33 states that don't prohibit workplace discrimination based on sexual orientation.
"This legislation," Heller said, "raises the federal standards to match what we have come to expect in Nevada, which is that discrimination must not be tolerated under any circumstance."
While it is likely the bill will pass the Senate, its prospects in the House remain doubtful. House Speaker John Boehner, R-Ohio, voiced opposition Monday to the nondiscrimination bill and may not bring it up for a vote.
"The speaker believes this legislation will increase frivolous litigation and cost American jobs, especially small-business jobs," Boehner spokesman Michael Steel said in an email to reporters.
The House version of the bill has 193 sponsors, including Rep. Jim Matheson, D-Utah. It takes 218 votes to pass a bill in the House.