House Republicans will move again on Tuesday to strip Rep. Charlie Rangel of his chairmanship of the powerful Ways and Means Committee — and after last week’s admonishment of the veteran New York lawmaker by the House ethics committee, Republicans are confident that they will be pick up more Democratic votes.

Rep. John Carter (R-Texas) will introduce a privileged resolution Tuesday on Rangel, according to John Stone, his spokesman.

Carter is hoping for a vote on the measure by Wednesday, Stone said...