WASHINGTON — Sen. Joe Lieberman on Tuesday warned “irrelevant amendments” could erode bipartisan support for a bill outlawing what has been termed “congressional insider trading.”

At a media briefing with Republican Sen. Scott Brown of Massachusetts and Democratic Sen. Kirsten Gillibrand of New York, Lieberman, an independent from Connecticut, said they worry that Senate Majority Leader Harry Reid’s decision to allow an open amendment process could mean the bill would be “smothered with kindness.”

The Senate agreed Monday to advance the STOCK Act, or the Stop Trading On Congressional Knowledge Act, to floor debate on a 93-2 vote. Senators consented to start debating by voice vote Tuesday morning.

“As always the case, when you give people freedom, you hope that people act with responsibility,” Lieberman told reporters. “Some of the amendments filed are relevant to the debate and some of them, to me, seem to be irrelevant.”

Some lawmakers have suggested amending the measure to cover other financial activities, which Lieberman said could scare off bipartisan backing.

In its current form, the STOCK Act would make clear that federal lawmakers cannot trade stocks using nonpublic knowledge gained from their time in Congress. It would effectively crystallize the Securities Exchange Act of 1934, which doesn’t explicitly state legislators cannot engage in such behavior.

President Barack Obama touted the measure in his State of the Union address last week, and the White House issued a statement applauding the Senate’s progress on the legislation Monday.

“While there’s more work to be done to eliminate the corrosive influence of money in politics, this is an important step to repair the deficit of trust between Washington and the American people,” White House press secretary Jay Carney wrote in the statement. “We urge Congress to pass this bill, and the president will sign it right away.”

The two senators who voted against proceeding with floor debate on the STOCK Act were Republicans Tom Coburn of Oklahoma and Richard Burr of North Carolina.

In an email Tuesday, Burr spokesman David Ward said the senator believes there are already laws in place dealing with the targeted issue.

“Members of Congress are elected to serve the people, not make money for themselves, and any member or staff member who breaks the already existing insider trading laws should be held responsible,” Ward wrote.

Brown, a sponsor of the bill along with Lieberman and Gillibrand, echoed the White House’s remarks at Tuesday’s press briefing, calling the STOCK Act a “good and strong start to closing our deficit of trust with the American people.”

Lieberman repeatedly cautioned the bill could get bogged down in the open amendment process. He said he hopes his Senate colleagues will be restrained in their amendment proposals and recognize there is a “very strong bipartisan majority that agrees with the basic points” of the STOCK Act.

“We could make it so perfect it fails, but I’m not excluding anything,” he said.

Gillibrand agreed the bill could still have “substantial teeth” without all-encompassing amendments.

“It’s simply not right,” she said of congressional insider trading. “Nobody should be above the rules.”