WASHINGTON -- Senate Majority Leader Harry Reid (D-Nev.) on Tuesday cleared the way for President Barack Obama to use executive action to ban workplace discrimination against lesbian, gay, bisexual and transgender federal contractors, as the issue stalls in Congress.

"If the president decides to do it, Id be in favor of it," Reid told The Huffington Post, in the halls of the Capitol.

A number of Democratic leaders think Obama should take action, since related legislation, the Employment Non-Discrimination Act, has hit a wall in the House of Representatives, where Speaker John Boehner (R-Ohio) says he won't give it a vote. The White House argues that executive action wouldn't go far enough , since Obama only has the ability to ban discrimination among government contractors, whereas legislation would apply to all employers.

Still, an executive order could protect as many as 16 million workers . And with Boehner standing in the way of ENDA, and with the president taking executive action on other issues currently awaiting votes in Congress, LGBT rights supporters are urging the president to get the ball moving. Right now, it is legal in 33 states for an employer to fire or harass someone for being LGBT.

HuffPost reached out to all 64 backers of the Senate ENDA bill, which passed in November, to see if they support the president using his executive authority on the issue. As of Tuesday, at least 20 senators responded to say they would support the move, although all said they would ideally like to see Congress pass the broader ENDA legislation.

Backers include Senate Majority Whip Dick Durbin (D-Ill.); Sen. Chuck Schumer (D-N.Y.), chairman of the Senate Democratic Policy Committee; Sen. Tom Harkin (D-Iowa), who chairs the Senate Committee on Health, Education, Labor, & Pensions, which pushed ENDA through; and Sen. Jeff Merkley (D-Ore.), who is the lead sponsor of the bill.

Sen. Chris Coons (D-Del.) compared an executive order on LGBT discrimination to President Harry Truman's integration of the military.

"Executive orders have long been a vehicle for progressive leadership on values," said Coons. "This is the sort of strong leadership that the President can exercise on progressive values within his constitutional authority. Presidents Truman and Johnson both used executive orders to lead the way on racial justice. Truman issued Executive Order 9981 to integrate the armed forces and Johnson issued Executive Order 11246 to ban racial discrimination in hiring by federal contractors."

Sen. Brian Schatz (D-Hawaii) noted that Obama taking executive action on the issue would be in line with his recent promise to be more aggressive using his own authority where Congress is deadlocked.

"If Speaker Boehner is committed to standing in the way of progress, then its appropriate for President Obama to move forward and do whats needed to make sure everyone in America, regardless of the gender of who they love, can go to work and earn a living for their family," he said. "The President just announced in the State of the Union that this is going to be the year of action, so I support him using his authority on the executive level to make sure Americans are protected from discrimination."

House Democratic leaders have already said unequivocally that Obama needs to act. Last week, House Minority Leader Nancy Pelosi (D-Calif.) said "of course" he should move forward. Rep. James Clyburn (D-S.C.), the third most powerful Democrat in the House, said he, too, feels "very strongly" about Obama acting and noted that it was an 1863 executive action by President Abraham Lincoln, the Emancipation Proclamation, that led to the end of slavery.

Not everyone on the Democratic side agrees with the strategy. Sen. Angus King (I-Maine), who caucuses with the Democrats , told HuffPost he was "uncomfortable" with the idea of an executive order to ban discrimination, while Sen. Joe Manchin (D-W.Va.) said "making policy is not [Obama's] prerogative."

Republicans also voiced their concern. Two GOP co-sponsors of the bill in the House -- Reps. Charlie Dent (R-Pa.) and Ileana Ros-Lehtinen (R-Fla.) -- said they would not back an executive order, and five of the 10 Republicans who voted for ENDA in the Senate said the same.

"In general, I was a big supporter of ENDA, and I prefer it as a legislative right rather than an executive order right," said Sen. Mark Kirk (R-Ill.), one of the bill's two GOP co-sponsors. "The problem is by executive order ENDA just will hang only on the president's opinion, that if we go so heavily to executive orders the next president of the next party will wipe out hundreds of executive orders by the Obama administration. That is a very shaky reed to hang basic human rights on."

Sen. John McCain (R-Ariz.) said if Obama uses executive authority too aggressively, it will "hurt any real bipartisanship."

But Sen. Rob Portman (R-Ohio) didn't rule it out support for executive action, saying he would "need to look at it." He added that he still believes the broader legislation could pass.

"I think maybe I'm wrong, but I think there's a chance that [ENDA] could get some support among Republicans in the House," he said.

This article has been updated throughout with comments from lawmakers.