Michael P. Aitken, vice president of government affairs for SHRM, also wrote in the letter that SHRM looks forward to working with congressional leaders on enacting "effective" and "responsible" health care reforms.

The letter "should resonate" with Republicans, particularly about the law's provisions that "burden employers," such as having to track and report on participants in health plans and having to pay per-employee penalties for noncompliance.

Aitken also suggests lawmakers "eliminate coverage requirements on employer-sponsored plans to ensure employers have the flexibility to design benefit plans that meet the unique needs of varying workforces" and "allow employers to adopt innovative strategies to improve health benefit offerings to lower overall U.S. health care costs."

No details have been released on possible replacements for provisions of the law, although several outlines have been proposed by individual Republican lawmakers. The president-elect has not issued specifics on any plan he may have in the works.

Once the budget resolution was passed, along party lines, committees of resolution were expected to begin work on drafts for budget and tax reconciliation legislation, including specific provisions to repeal taxes imposed by the ACA.