Democrats are boasting that several Republicans are expected to defy their leadership team.
The Supreme Court ruled that a government task force that determines what preventive health care services insurers must cover at no cost under the ACA is constitutional.
During his campaign, Trump vowed to make the Affordable Care Act "better" and to protect "women." He also suggested that Robert F. Kennedy Jr. would shape the public health agenda of his administration.
When asked by ABC News moderator Linsey Davis to clarify if he had a health care plan, the former president said he had "concepts of a plan" to replace the ACA but provided no details.
The special enrollment period that allows the uninsured to pick Affordable Care Act policies ends Sunday.
Many observers see as a likely outcome that the court could simply "sever" the individual mandate from the law and leave the rest alone.