The House moved Tuesday toward approving a measure aimed at softening legislation responding to the 2008 financial crisis that put banks and Wall Street under the most sweeping rules since the Great Depression.

Amid a veto threat from the White House, the legislation pushed by the newly bulked-up Republican majority came under discussion in the House for the second time in less than a week. This time it's likely to pass, with a vote expected Wednesday that will advance a key Republican priority.

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

On the House floor, Democratic lawmakers 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 also were blocked late Monday from bringing about a dozen proposed amendments to a vote on the floor.

Republicans insisted that since most of the provisions of the bill already had been voted by the House in the last Congress as separate measures, there has been ample opportunity 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.

"Just one week after being sworn into office, the House of Representatives is already showing the American people that its priorities are all wrong," Dennis Kelleher, president of Better Markets, a group that advocates strict financial regulation, said in a statement.

The bill won a 276-146 majority in the House last Wednesday — 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 U.S. financial industry.

As passage appeared closer, the Obama White House issued a formal 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.