Senators, speaking anonymously, said the panel has lost power in recent years under Inouye, 88, who took over the chairmanship after Democrats pressured Sen. Robert Byrd, D-W.Va., to relinquish the post in 2008, The Hill reported Friday.
"I love Inouye," one Democratic senator said. "He's just been sort of not there in terms of running the committee. ... We get shunted to the side; we don't get our bills out; we're not forceful about it. I guess that argues for term limits. Sometimes people stay just too long."
Some senators expressed frustration that the Appropriations Committee has become what they consider a rubber stamp for the Obama administration's priorities.
Discussion about whether the Appropriations Committee should have a new chairman is part of a broader debate about whether Senate Democrats should place term limits on committee chairmen, The Hill said. Republicans imposed six-year term limits on committee chairmen in 1995, as well as limiting service as a committee's ranking minority member to six years.
"People are talking about different things," said Sen. Claire McCaskill, D-Mo., declining to discuss Inouye specifically. "I think we're struggling to find a way to make sure everyone can contribute, but it's too early to say anyone is leading anything in one direction. People are just talking."
Senate Majority Leader Harry Reid has resisted imposing term limits on chairmen, telling The Hill "No" when asked if he'd support limits.
Inouye, who experienced difficulty breathing this week and is recovering at Walter Reed National Military Medical Center, told The Hill in a statement he appreciated the confidence of the Democratic Steering Committee, which announced his reappointment this week.
"Over the past four years the committee has accomplished a great deal, from enacting the American Recovery Act and the final war supplemental during my first 120 days as chairman to enacting all 12 bills in fiscal year 2012 and reporting 11 of our 12 bills to the floor for the current fiscal year," he said.