National Republican Senatorial Committee Chairman John Cornyn said he's open to discussions on a ban on earmarks but that the public might better be served by looking at other ways to address jobs and debt.
Earmark opponents may have scored some successes in recent years, but several Senators said they remain wary of permanently giving up the right to direct spending and would rather focus on other business.
"I think we need to talk about that," National Republican Senatorial Committee Chairman John Cornyn (R-Texas) said. "I am not sure we need it, but I am open to it."
He continued, "I wish we would focus on what the American people are most concerned about rather than some of these other issues that have their importance but are tangential to the main issues we ought to be focused on."
"I think we ought to [instead] be looking at other ways to ... address people's concerns about jobs and the debt," Cornyn said.
The Senate could vote this week on a proposal by Sens. Claire McCaskill (D-Mo.) and Pat Toomey (R-Pa.) to make the current moratorium on earmarks permanent. They've offered the measure as an amendment to legislation banning insider trading by lawmakers and their staff.
"Earmarks exist precisely to circumvent ... [Congressional] scrutiny," Toomey said Tuesday on the Senate floor.
He said that while many earmarks are worthy of being funded, "There is an opportunity for corruption. A process like that is badly flawed and should be remedied."
The amendment would also create a point of order to strike earmarks from bills, and it would take two-thirds majority to override that point of order.
On the floor Tuesday, McCaskill said she wants to "stop the process in its entirety" rather than going after individual earmarks.
"I am proud of the fact that we have a moratorium," she said. "But there are a lot of Members of this body that want to go back to the old ways."
Still, earmark supporters said that the issue is purely political.
"It's just stupid, it's childish, it's demagoguery," Sen. James Inhofe (R-Okla.) said. "There is not a lot of courage in our conference [on the issue.] They all know better. They all know by banning earmarks ... they are just giving the authority to the president. But they are afraid of it because people don't understand the issue out there."
Sens. Mark Begich (D-Alaska), Dick Lugar (R-Ind.) and Ben Nelson (D-Neb.) said they would stand up to support their right to earmark if the amendment was brought to the Senate floor.
But it's unclear whether the amendment will get a vote.
"I hope we get a vote, but I am not optimistic," McCaskill said.
Senate Majority Leader Harry Reid (D-Nev.) on Tuesday would not say whether he would permit a vote on the proposal and gave a firm defense of earmarking.
United We Dream protesters carry a mock coffin to the office of Sen. Ted Cruz, R-Texas, in the Dirksen Senate Office Building on Monday, July 21, 2014, to hold one of their "funeral services for the Republican Party" due to GOP positions on immigration. The immigration reform group visited several other Senate Republican offices to hold similar funeral services.