Democratic leaders argue that a majority of Americans favor both steps, which are priorities for President Barack Obama, and say the House GOP is the obstacle. Republicans say Democrats are embarking on an approach that they know has little chance of success in an attempt to circumvent the will of the GOP-led House.
The odds are daunting for Democrats in what clearly is political maneuvering ahead of the elections this fall.
Some questions and answers on how it works.
Q: What does a discharge petition do?
A: It allows the minority or opposition party to bypass the House speaker and get a vote.
First, 217 members — one more than half the House's current membership of 432 — have to sign a petition. A motion to consider the wage issue would then be placed on the legislative calendar, but it can't be acted on for at least seven days. Any lawmaker can then call it up but only on the second or fourth Monday of the month. The motion is debated and if the House passes it, then lawmakers would consider and vote on the bill.
Currently there are 232 Republicans, 200 Democrats and three vacancies in the House. All 200 Democrats would have to sign the petition, but Democrats would have a tough time getting 17 Republicans to join them.
Signing a discharge petition would be a breach of loyalty for Republicans, certain to draw the wrath of the caucus, and a rebuke of Speaker John Boehner, R-Ohio.
Republicans largely oppose any increase in the minimum wage. They say it's an issue left to the states and that it could slow hiring in a struggling economy.
Rep. Steny Hoyer of Maryland, the No. 2 House Democrat, acknowledged that Democrats are unlikely to sway Republicans. Yet he also provided a preview of one of his party's arguments on this issue.
"I don't think we're ever confident that we're going to get 18 Republicans to sign a discharge petition, but we apparently have 30 or 40 that are known over here," Hoyer said at a news conference this past week at the party's retreat in Cambridge, Md. "Our expectation is if they want to make sure that working people have an incentive to work, they will pay them to do so a wage that does not leave them in poverty."
Q: What about immigration? A number of House Republicans back a comprehensive approach. Would they sign a discharge petition?