The Choice Act would exempt some financial institutions that meet capital and liquidity requirements from many of Dodd-Frank’s restrictions that limit risk taking. It would also replace Dodd-Frank’s method of dealing with large and failing financial institutions, known as the orderly liquidation authority — which critics say reinforces the idea that some banks are too big to fail — with a new bankruptcy code provision.

In addition, the legislation would weaken the powers of the Consumer Financial Protection Bureau. Under the proposed law, the president could fire the agency’s director at will and its oversight powers would be curbed.

The bill would also eliminate the Labor Department’s fiduciary rule, which requires brokers to act in the best interest of their clients when providing investment advice about retirement. The first parts of the rule are scheduled to go into effect on Friday. The rule was completed last spring under Mr. Obama after years of development.

According to an analysis by the Congressional Budget Office, the Financial Choice Act would reduce federal deficits by $24.1 billion over a decade. The budget office cautioned, however, that there was considerable uncertainty in its estimates because it was difficult to predict when a “systemically important” financial firm might fail.

Business lobbyists and conservative think tanks have been largely supportive of the plans, which they argue will ease lending and help small companies create jobs.

“The 2010 Dodd-Frank Wall Street Reform and Consumer Protection Act is among the most inappropriately named laws ever enacted in the U.S.,” said Norbert Michel, a Heritage Foundation research fellow. “It neither reformed Wall Street nor protected consumers, and it imposed massive new regulations on banks far away from Wall Street.”

Optimism about big changes remains tempered, however.

While expressing polite, if restrained, gratitude to Representative Jeb Hensarling, the Texas Republican who championed the dismantling of Dodd-Frank for years, banking lobbyists were realistic about actual changes the Senate Democrats would be willing to swallow.