(WASHINGTON, AP) — More than six years after the financial crisis struck, the House is moving toward softening a post-crisis law that brought the strictest rules for banks and Wall Street since the 1930s.

Under a veto threat from the White House, the bill pushed by the newly bulked-up Republican majority came under discussion in the House on Tuesday for the second time in less than a week. This time it’s likely to pass, with a vote expected Wednesday that would advance a Republican priority.

The bill would alter sections of the 2010 Dodd-Frank financial overhaul. Most notably, it would give U.S. banks two extra years — until 2019 — to ensure that their holdings of certain complex and risky securities don’t put them out of compliance with a new banking rule.

In debate Tuesday night in a nearly empty House chamber, Democratic lawmakers denounced the move as a giveaway to the largest U.S. banks, which hold the bulk of the securities in question.

Rep. Maxine Waters of California, senior Democrat on the House Financial Services Committee, called it “this gift to a handful of the biggest Wall Street banks.”

The bill’s author, Rep. Michael Fitzpatrick, R-Pa., insisted it makes “smart, technical reforms.” It would have the effect of “reining in out-of-control Washington regulators” and helping small businesses create jobs by reducing their compliance burden, Fitzpatrick said.

The Democrats also objected to the measure being whisked through the House in the first days of the new Congress without the chance for discussion or changes at the level of congressional committees. The Democrats were blocked late Monday from bringing about a dozen amendments to a vote on the floor.

Republicans insisted that because most of the provisions of the bill already had been voted on by the House in the last Congress as separate measures, ample opportunity was provided to consider them.

The bill would revise the so-called Volcker rule, a key part of the financial overhaul law, which would limit banks’ riskiest trading bets. That kind of risk-taking on Wall Street helped trigger the 2008 crisis.

The bill won a 276-146 majority in the House a week ago — only the second day of the new Congress — but failed under fast-track rules that required a two-thirds vote. This time it’s likely to pass under rules that require a simple majority.

Republicans in the House have been trying for years to chip away at the Dodd-Frank law, which Congress enacted with mostly Democratic support to tighten regulation with an eye to preventing another crisis. Republicans have denounced the law as an excessive expansion of regulatory authority that’s stifling the competitiveness of the financial industry.

As passage appeared closer, the Obama White House issued a veto threat Monday, saying the bill “would weaken and undermine” the Dodd-Frank law. Referring to the proposed two-year delay for certain securities under the Volcker rule, the White House said in a statement, “taxpayers should not have to wait that long to have limits in place that protect them from risky practices.”

The Federal Reserve in April gave banks until July 2017 to sell off their holdings of so-called collateralized loan obligations, which are mainly backed by commercial loans to higher-risk companies. That came atop a previous one-year extension by the Federal Reserve, to July 2015.

The rule is named for Paul Volcker, a former Fed chairman who was an adviser to President Barack Obama during the financial crisis. Volcker urged a ban on high-risk trading by big banks to diminish the likelihood that taxpayers might have to rescue them, as they did after the crisis, with hundreds of billions of dollars in government aid.