Four Republican senators — enough to thwart passage — said Thursday they will not support the current Senate Obamacare replacement plan and will seek changes.

Conservatives Rand Paul of Kentucky, Ted Cruz of Texas, Ron Johnson of Wisconsin and Mike Lee of Utah said in a statement that they "are not ready to vote" for the proposal Senate Republicans released Thursday.

"There are provisions in this draft that represent an improvement to our current health care system, but it does not appear this draft as written will accomplish the most important promise that we made to Americans: to repeal Obamacare and lower their health care costs," the senators said.

Paul told reporters that "my hope is not to defeat the bill, but to make the bill better." He said, "We want the bill to look more like a repeal."

Cruz told reporters that "I think we can get there, but the current draft doesn't do nearly enough."

Senate Republicans on Thursday morning released a draft of their secretive Obamacare replacement bill, called the "Better Care Reconciliation Act of 2017." The plan would repeal Obamacare taxes, restructure subsidies to insurance customers that are based on their incomes and phase out Medicaid's expansion program. It contains some key differences from the version the House passed last month.