In the memo, Cantor wrote: "American families have enough to worry about as we enter the new year without having to wonder if they can trust the government to inform them when their personal information -- entered into a government mandated website -- has been compromised," House Republican Leader Eric Cantor said in the memo to colleagues on Thursday. 

Cantor cited widespread warnings that personal information could be breached after it's entered into the new health law system, said Reuters. One recent report from data company Experian cautioned that the millions entering the insurance exchanges will "increase the vulnerability of the already susceptible healthcare industry." 

Experian warned that the industry, "by far, will be the most susceptible to publicly disclosed and widely scrutinized data breaches in 2014." 

An administration spokesman responding to Cantor's memo said that security on the website was a top priority and was protected by stringent standards as well as ongoing testing, said Reuters.

"To date, there have been no successful security attacks on HealthCare.gov and no person or group has maliciously accessed personally identifiable information from the site," said Aaron Albright, a spokesman at the Centers for Medicare and Medicaid, which was in charge of launching HealthCare.gov.

Under current policy, an agency within the Department of Health and Human Services is tasked with deciding whether there is a risk of harm and whether individuals need to be notified whenever a security breach occurs,

Under current policy, an agency within the Department of Health and Human Services is tasked with deciding whether there is a risk of harm and whether individuals need to be notified whenever a security breach occurs, said Reuters. Republican lawmakers argue that the notification should not be optional. 

Cantor, in his memo, likened the risks surrounding HealthCare.gov to the recent data breach at Target, said Reuters.