Sen. Tom Harkin is among the chairmen who might be vulnerable if gavels were to be decided by a full Democratic caucus vote.
“I don’t see huge momentum behind it,” one Democratic aide said.
During the leadership meeting, sources said, Reid urged those present to oppose the measure; however, he did not repeat those sentiments during the caucus meeting that afternoon.
Even if supporters choose to try to push the matter to a vote, several sources said it would likely fail because of the divergent views.
The changes to internal caucus rules will be dealt with after the Senate recess.
Traditionally, both parties have operated under a system where chairmen are chosen by seniority, leaving junior Members to wait years and sometimes decades before chairing a major panel.
Although Republican committee members vote individually on their chairmen, it is rare for popularity to trump seniority.
In addition to alienating newer Members, this system can present other problems, such as elderly chairmen hanging onto positions long after they are able to fulfill their duties.
In the past 15 years, then-Appropriations Chairman Robert Byrd (D-W.Va.) and then-Armed Services Chairman Strom Thurmond (R-S.C.) bowed to pressure to step down because of their age and health.
Members of the classes of 2006 and 2008 have expressed impatience with the seniority system and have been eager to get their hands on gavels so they can influence legislation.
The reform effort is a part of a broader push by Members who were elected in recent cycles to reform both internal caucus and Senate rules to equalize the stature of Democratic Members and make the chamber more “efficient.”
In the last Congress, Reid made an effort to give subcommittee gavels to 2006 class Members in particular, but tighter ratios during the 112th Congress may force some of those Members to step down from panels.
Republicans and some senior Democrats have criticized some of the changes, saying they dilute the power of the minority party and make the Senate too much like the House.
Rep. Elijah Cummings, D-Md., right, hugs Harold Schaitberger, General President of the International Association of Fire Fighters, after the Congressman spoke at the IAFF's Legislative Conference General Session at the Hyatt Regency on Capitol Hill, March 9, 2015. The day featured addresses by members of Congress and Vice President Joe Biden.