The practice has come under fire from Democrats who say it is connected to the "K Street Project," an initiative to bolster GOP ties to lobbyists.
CBS News correspondent Bob Fuss reports it has been a longtime practice where lobbyists were made part of the leadership team, urged to give campaign money to Republicans and pressured to hire Republicans for key jobs.
Republicans denied on Thursday that there is a connection between the Capitol Hill meetings and the K Street Project. But they said the job-seekers list will no longer be circulated to avoid misunderstandings about the nature of the bimonthly meetings.
Critics say the K Street effort — named after the street where many lobbyists work — created an atmosphere that led to the excesses exhibited by lobbyist Jack Abramoff, who has pleaded guilty to federal corruption charges.
Staff members from the Senate Republican Conference — the organization of GOP senators that sets Senate Republican policy — notified the Republican National Committee on Wednesday that the practice of distributing a list of potential hires put together by the RNC would end, said Robert Traynham, a spokesman for Sen. Rick Santorum, chairman of the Senate Republican Conference.
The decision was made "so that people don't misconstrue the point of our meetings," said Barbara Ledeen, director of coalitions at the SRC. "It's redundant to do that. The RNC already does it."
Among Senate Democrats, Phil Singer, a spokesman for the Democratic Senatorial Campaign Committee, said any distribution of job lists has not gone on for some time.
Every other Tuesday when Congress is in session, Santorum, R-Pa., meets with lobbyists and industry experts to discuss legislation.
"That's what the project that I've been involved with has been about, period, is making sure that we're able to get our message out," Santorum said at a recent news conference. "It has not been about putting pressure on people to hire individuals."
Santorum, who is trailing his likely Democratic opponent Pennsylvania Treasurer Bob Casey in his November bid for re-election, was asked by Senate Majority Leader Bill First to craft lobbying reform legislation.
Democrats have said that it is hypocritical that Santorum — who has received more money from lobbyists than any other 2006 incumbent — is leading the effort, and they have accused him of being the Senate liaison to the K Street Project, which Santorum denies.
"You want to have real reform? Kill the K Street Project," House Democratic leader Nancy Pelosi said. "Yes, ban the travel, ban the gifts, stop the revolving door."
Also Thursday, two Senate Democrats are calling for a special counsel to take over the investigation of the corruption scandal involving lobbyist Jack Abramoff.
New York Senator Charles Schumer and Colorado's Ken Salazar wrote to Attorney General Alberto Gonzales that the change would give the public "full confidence" that "no one in this country is above the law."
The letter was sent several days after Democrats pressed the White House for information on contacts between the president or other top officials and Abramoff.
The White House hasn't released any photographs of the president and Abramoff together. Bush says it's because the pictures would be "used for pure political purposes."
Abramoff pleaded guilty earlier this year to several felony charges, some of which involve his dealings with members of Congress and their aides.
On Thursday, Grover Norquist, who founded the K Street Project, said the job lists that circulated on Capitol Hill were separate from his effort.
Norquist, president of Americans for Tax Reform, said the actual K Street Project is an ATR-financed Web site that lists job openings and tracks hiring. He said the goal is to encourage trade associations and businesses to hire lobbyists with compatible views, who tend to be Republican.