Sen. Ted Cruz, R-Texas, said Sunday he has not yet been won over to support the last-ditch Republican effort to overhaul Obamacare.

"Right now, they don't have my vote and I don't think they have Mike Lee's either," Cruz said at a Texas Tribune event, referring to his conservative colleague from Utah. "I want to be a yes, I want to get there because I think that Obamacare is a disaster. But the price to getting there, I believe, is focusing on consumer freedom."

Cruz suggested the reason he opposed the bill was because it woudn't do enough to lower prices of health insurance.

"If you want prices to go down you want more choices, more options, more competition and prices fall," he said. "What does Obamacare do? Fewer choices, less options, less competition, prices rise. If you want people to have access to health insurane, you want prices to fall."

The bill is sponsored by GOP Sens. Lindsey Graham of South Carolina, Bill Cassidy of Louisiana, Dean Heller of Nevada and Ron Johnson of Wisconsin, and would transfer Obamacare's revenue to states in the form of block grants. It also would repeal the individual and employer mandates.

Senate Majority Leader Mitch McConnell has said he intends to bring the bill to the floor for a vote early this week. Two Republican senators have said they oppose the bill, including Rand Paul of Kentucky and John McCain of Arizona, and Sen. Susan Collins of Maine has said it was difficult to envision voting for it.

The combination of three Republicans voting against the bill as well as opposition from all Democrats against the bill, known as Graham-Cassidy, would doom its passage. No Democrat has said he or she would support the legislation.