Washington (CNN) The House of Representatives kicks off two days of hearings Wednesday on whether to bring back so-called earmarks following a seven-year moratorium.

One week after President Donald Trump threw his support behind the idea, the Rules Committee will hold already-scheduled hearings on Wednesday and Thursday.

Rep. Pete Sessions, the committee's chairman, believes lawmakers can revive the practice of tagging specific projects in spending bills.

"Yes, I do believe we can get there," Sessions told reporters, though he insisted they aren't talking about "earmarks" but "legislating specifically on projects."

Following examples of abuse and runaway spending, former House Speaker John Boehner banned earmarks when the GOP regained control of the House of Representatives in 2011.

Critics still fear public opposition to the idea of returning to earmarked spending, especially heading into an election year.

"We got beaten like a borrowed mule in the 2006 elections largely because of the corruption that came with earmarks," Sen. Jeff Flake, R-Arizona, said last week. "People are forgetting that time. It was awful; we don't want to go back to that."

Trump raised the issue at a bipartisan meeting earlier this month with lawmakers at the White House, saying earmarks helped facilitate better cooperation between the two parties in Congress because members were more willing to compromise if they could get earmarked funds for their pet projects.

Sessions argued there is a "lightyear's difference" between the previous system and the system being considered now.

"This is draining the swamp. If you think that we are going back to where we were, we have missed the boat," Sessions said. The reformed process he's pushing, he added, would not look like the "earmarks" of the past that sparked public backlash, when thousands of projects were inserted into funding bills for items that many considered wasteful.

"No more surprises, no more secrets," the Texas Republican said.

Any changes, he stressed, would require a more transparent process in which members must attach their names and publicly argue for their requests. Members would also not be able to "airdrop" projects into a bill already worked out through a committee process.

He also vowed that any projects added to legislation would be "merit-based." It's unclear if Republicans do agree to make a change and whether it would come in next year's spending bills, which they will begin working on shortly.

Under the old system, lawmakers were attacked for pushing for projects like the so-called "bridge to nowhere," an earmark for a bridge costing more than $200 million to build to link a road to a remote Alaskan town with a tiny population. This time, Sessions noted "there's not exactly enough money to go splashing around." He said with fewer resources available to dole out to states and local governments, members will need to compete to get items in bills.

"We're for making sure that everybody has a chance and the best project, I should say projects, should win," Sessions said.

The Rules committee hearing on Wednesday will feature roughly a dozen lawmakers from both parties, including Florida GOP Rep. Tom Rooney, who pressed last year for the House to end the moratorium on specific funding projects, and the number two House Democrat, Rep. Steny Hoyer. On Thursday, the committee will hear from a group of outside experts on the issue.

The committee plans to take input from members across the spectrum of the conference and make a recommendation on whether to change existing rules.

To bring back the practice, the House GOP conference would first need to approve updating its internal rules, and then any modification would need to be approved in a vote by the full House of Representatives. Even though some Democrats support reviving earmarks, it's likely they will force Republicans to take ownership of the issue and carry any resolution on the House floor.

Shortly after the 2016 election, Ryan attempted to quash the idea of reviving earmarks, saying it wasn't the right time. "We just had a 'drain the swamp' election," Ryan told Republicans. "Let's not just turn around and bring back earmarks two weeks later."

Ryan helped lead the charge to ban earmarks back in 2011, and his spokeswoman, AshLee strong, says he still opposes them. However, he reached an agreement that the conference could have "have an open and honest conversation" as long as it was in public, rather than behind closed doors.