Hours after the Labor Department unveiled significant amendments to the final version of its fiduciary rule, several Republican members of Congress vowed to roll back the new regulations – though the likelihood of success is low.

Rep. Jeb Hensarling (R-Texas), the chairman of the House Financial Services Committee, says the rule will harm millions of Americans by raising the costs of financial planning. He urged his fellow congressmen to overturn the "unfair" regulation.

"This is Obamacare for your IRA and 401(k), and just like Obamacare this complex rule will likely raise your costs and potentially limit your choices," Hensarling said in a statement.

Rep. Ann Wagner (R-Missouri), who serves on the same committee, also called on her colleagues to "to stop this ill-advised rule."

Other Republicans, such as Rep. Lynn Jenkins of Kansas, took to social media to show their disapproval.

"The #FiduciaryRule is regulatory overreach at its height. Families don’t need more mandates. They need more information," Jenkins tweeted.

Congress has an opportunity to vote to rescind regulations under the Congressional Review Act of 1996.  However, like previous legislative attempts to stop the Labor Department's efforts, this would not likely succeed in this Congress. For example, a bill put forward by Wagner last year failed to pass both houses.

If House and Senate majorities voted to overturn the rule, the measure would face a certain veto from President Obama, who has championed the rule.

Several leading Democrats – including Sens. Elizabeth Warren of Massachusetts and Cory Booker of New Jersey – were present at a Labor Department event on Wednesday to announce the details. Booker cautioned fiduciary supporters that there would be pushback.

"This fight is not over. ...Rules have been attacked before, rules have been rolled back," Booker said.

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