Sen. Mitch McConnell slammed Democrats, suggesting they flip-flopped on the legislation.
The legislation is spearheaded by Ben Cardin, a Democrat who opposed the Iran deal.
Proposal includes some reductions in mandatory minimum sentencing.
The calls from Senate Democrats are fallout from comments by Kevin McCarthy.
Previous reports say some U.S. troops were told to ignore abuse of young boys by Afghan forces.
The Texas Republican wants to designate Iran's Revolutionary Guard as a foreign terrorist organization.
Sen. Chuck Grassley is currently blocking 22 State Department nominees.
The request comes as Russia is stepping up its military activity in Syria.
The proposal will include targeted sentencing reforms, according to an aide.
The move could undercut President Obama's nuclear deal with Iran.