Senate Republican Leader John McKinney is calling for Governor Malloy to convene a special session of the General Assembly.
McKinney said Friday only the state legislature can authorize the fix to the health care law that President proposed.
"Connecticut cannot implement the president's request that if they like their plan they can keep it," said Sen. McKinney.
He said that's because a 2011 law passed by the General Assembly requires insurance companies in the state to comply with the Affordable Care Act.
"This statute says that you cannot sell an insurance product that does not comply with the Affordable Care Act," he said.
On Thursday President Obama reversed course after millions were dropped from their current plans since those plans were no longer compliant with Obamacare.
Insurance companies have already set rates to be compliant with ACA. They warned on Thursday that the President's "fix" could drive up premiums.
"What I worry about in this change is that it adds yet another layer of confusion on top of an already confusing situation," said Mitchell D. Weiss, Professor of Finance at the University of Hartford.
Some experts believe this will create even bigger problems for the law because people may not head to the exchanges if they get their current plans back.
Connecticut's insurance exchange, Access Health CT released new numbers on Friday showing more than 13,000 have enrolled. They are watching what's happening closely.
"We're waiting to see what the insurance department and we will obviously comply," said Kevin Counihan, CEO of Access Health CT.
The Connecticut Insurance Department said late Friday they are still weighing their options.
"In the wake of the decision yesterday in Washington, the Governor has asked the Lieutenant Governor and his Insurance Commissioner to gather the facts and determine what action, if any, needs to be taken by the state to ensure we are achieving this goal," said Andrew Doba, Director of Communications for Governor Malloy. "Until all the facts are in, there is no reason to call a special session.”