Dodd had managed the HELP committee in the absence of Sen. Edward Kennedy (D-Mass.), who passed away late Tuesday night, in addition to his responsibilities as chairman of the Senate Banking Committee.
Republican state Sen. Sam Caligiuri, a GOP primary candidate to face off against Dodd, demanded the incumbent Democrat reject taking over the HELP committee.
"I am calling on Senator Dodd to decline the position of the HELP Committee Chairman, if it is offered to him," Caligiuri said in a statement. "He should be finishing the job he has barely started of fixing the financial sector problems that got us into this economic disaster in the first place, and not spending his time promoting ill advised health care legislation."
Dodd said earlier today in a teleconference that he wasn't sure what his status with the committee would be going forward, and that it would take a few weeks to sort it out.
"Only in Washington would someone who failed miserably at one crucial job be considered for taking the reins on another important front," Caligiuri said. "In typical DC fashion, Senator Dodd is all politics all the time, hoping to secure this new post to dust his past failures under the rug and forge ahead with yet more bad legislation."