A bipartisan group of four lawmakers renewed a push Tuesday to impose a permanent ban on congressional earmarks, the line-item spending measures that have often been dedicated to narrow projects favored by a single member of Congress.

Citing a report Tuesday in The Washington Post that highlighted lawmakers who have sponsored more than $300 million worth of earmarks close to their personal property, two senators and two House members are pressing lawmakers to permanently halt the practice and do away with the current moratorium that House Republicans secured a year ago.

“Regardless of what you think about any particular circumstances, there’s an appearance of a problem, and that in itself is a problem,” Sen. Patrick Toomey (R-Pa.), who along with Sen. Claire McCaskill (D-Mo.) received only 40 votes for such a measure last week. “It’s just very important that we change the culture in this town.”

The outlook for an earmark ban remained dim Tuesday, however, as House and Senate leaders say the current moratorium is sufficient. Moreover, with the House slated to debate ethics legislation dealing with conflicts of interest on Thursday, lawmakers pushing that package of bills split this week over the best course of action.

Some want the most expansive legislation possible to cover a broad collection of potential conflicts and give greater transparency, while others fear that a larger ethics package would only get bogged down in parliamentary hurdles. They want to keep the focus on the original legislation, which forbids members of Congress and their staff from making financial trades based on private information they have learned while serving in their positions.

“The problem is, you start punching too much [into the bill], then you get the problem of it bogging down and not getting done,” Rep. Tim Walz (D-Minn.) said, arguing for a narrower piece of legislation that bans insider trading and requires more disclosure of consulting firms in Washington.

The Senate last week approved the insider trading ban but tacked on a series of measures to include senior members of the executive branch. In addition, the chamber passed by voice vote an amendment from Sen. John McCain (R-Ariz.) that forbids senior executives of the mortgage giants Fannie Mae and Freddie Mac from receiving bonuses. Another amendment requires members of Congress and top members of the executive branch to disclose information on mortgages for their primary residences, after it was reported that a half-dozen lawmakers and former Cabinet members received VIP mortgages from Countrywide Corp. in the last decade.

And members of the Senate Judiciary Committee won inclusion of language that would reinstate portions of a public corruption law that the Supreme Court last year ruled unanimously was unconstitutionally vague.

The Senate rejected the Toomey-McCaskill amendment to permanently ban earmarks, with senior senators defending their constitutional right to control the power of the federal purse.

“We have an obligation as members of Congress to fulfill our constitutional duty. One one of those duties is to make sure that we do congressionally directed spending,” Senate Majority Leader Harry M. Reid (D-Nev.) said before last week’s vote. “I object and do not believe that all these decisions should be made at the White house, whether it’s Obama as president or whether it was one of the Bushes as president. I do not accept that.”

As of late Tuesday, House Majority Leader Eric I. Cantor (R-Va.) was still crafting the version of the bill that his chamber would consider, most likely on Thursday. Cantor indicated to reporters early Tuesday that his goal was to focus the legislation on its original intent, saying that he wanted “to make it known that we feel it is unacceptable for anybody in this body to profit personally from non-public information.”

But some lawmakers continued to pursue a more expansive bill.

“I don’t think the bill, as it left here, is an unreasonable piece of legislation,” McCaskill said, pressing for the House to hold a vote on the earmark ban.

Rep. Jeff Flake (R-Ariz.), working for the earmark ban with Rep. Jim Cooper (D-Tenn.), cited the Post stories as reason for holding the most expansive debate possible on the ethics legislation.

“There is little arguing that stories like these, of which there seems to be no end, cast a shadow over Congress at a time in our history that would necessitate the utmost in trustworthiness with respect to fiscal matters. They allow for the appearance of impropriety that demands remedy,” Flake wrote in a letter to House Speaker John A. Boehner (R-Ohio) and Cantor. “It would seem inconsistent for Congress to take steps to address the public’s concern over the appearance that Members are making themselves richer via their positions with respect to financial transactions while ignoring the very same appearance with respect to earmarking.”