Originally Published: 01 MAR 23 15:55 ET

Updated: 01 MAR 23 16:54 ET

By Ali Zaslav, Clare Foran and Ted Barrett, CNN

(CNN) -- The Senate passed a politically charged resolution on Wednesday to overturn a Biden administration retirement investment rule that allows managers of retirement funds to consider the impact of climate change and other environmental, social and governance factors when picking investments.

Republicans complain the rule is "woke" policy that pushes a liberal agenda on Americans and will hurt retirees' bottom lines, while Democrats say it's not about ideology and will help investors.

The measure, which would rescind a Department of Labor rule, will next go to President Joe Biden's desk as it was passed by the House on Tuesday. The administration, however, has issued a veto threat. As a result, passage of the resolution could pave the way for Biden to issue the first veto of his presidency.

Opponents of the rule could try to override a veto, but at this point it appears unlikely they could get the two-thirds majority needed in each chamber to do so.

The resolution, authored by GOP Sen. Mike Braun of Indiana, only needed a simple majority to pass. Republican lawmakers advanced it under the Congressional Review Act, which allows Congress to roll back regulations from the executive branch without needing to clear the 60-vote threshold in the Senate that is necessary for most legislation.

Democrats control a narrow 51-to-49 majority in the Senate, meaning Republicans needed some cross-aisle support to pass it. Democratic Sen. Joe Manchin of West Virginia is a co-sponsor and Montana Democratic Sen. Jon Tester announced Wednesday he would vote for it. Both are up for reelection in red states next year.

Opponents of the rule have argued that it politicizes retirement investments and that the Biden administration is using it as a way to push a liberal agenda on Americans.

"The Biden Administration wants to let Wall Street use workers' hard-earned savings to pursue left-wing political initiatives," Senate GOP leader Mitch McConnell said in remarks on the Senate floor on Tuesday morning.

Republican Sen. John Barrasso of Wyoming said at a news conference on Tuesday, "What's happened here is the woke and weaponized bureaucracy at the Department of Labor has come out with new regulations on retirement funds, and they want retirement funds to be invested in things that are consistent with their very liberal, left-wing agenda."

Supporters of the rule argue that it is not a mandate -- it allows, but does not require, the consideration of environmental, social and governance factors in investment selection.

Senate Majority Leader Chuck Schumer said on Wednesday that Republicans are "using the same tired attacks we've heard for a while now that this is more wokeness. ... But Republicans are missing or ignoring an important point: Nothing in the (Labor Department) rule imposes a mandate."

"This isn't about ideological preference, it's about looking at the biggest picture possible for investments to minimize risk and maximize returns," he said, noting it's a narrow rule that is "literally allowing the free market to do its work."

The statement of administration policy saying that Biden would veto the measure similarly states, "the 2022 rule is not a mandate -- it does not require any fiduciary to make investment decisions based solely on ESG factors. The rule simply makes sure that retirement plan fiduciaries must engage in a risk and return analysis of their investment decisions and recognizes that these factors can be relevant to that analysis."

Republicans are also working to advance a measure to rescind a controversial Washington, DC, crime law -- which critics argue is soft on violent criminals -- with a simple majority vote in the Senate.

Many Democrats oppose overriding the DC law. They argue local officials should make their own laws free of congressional interference and decry Republicans as hypocrites since they typically promote state and local rights.

A Senate vote on the DC measure is expected next week.

This story and headline have been updated with additional developments.