Sen. Ted Cruz Rafael (Ted) Edward CruzMurkowski: Supreme Court nominee should not be taken up before election Battle lines drawn on precedent in Supreme Court fight Sunday shows - Ruth Bader Ginsburg's death dominates MORE (R-Texas) said on Sunday that he isn't yet ready to support the latest GOP effort to repeal and replace ObamaCare, increasing uncertainty that Republicans will be able to pass the legislation.

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"Now, I want to be a yes," he added, indicating a willingness to be won over.

"We said if you take these edits we're a yes. They took our edits and then a day later they removed our edits," Cruz said.

Both Cruz and Lee have sounded optimistic about the Cassidy-Graham legislation, but held off from offering their support and noted they are pushing for additional changes.

The ongoing negotiations reflect the uphill challenge GOP leadership faces to getting an ObamaCare repeal bill through the Senate by the end of the week.

Republicans have until the end of the month to pass an ObamaCare repeal bill by a simple majority. The budget rules allowing them to bypass a Democratic filibuster expire on Sept. 30.

Cruz, on Sunday, argued that was a "bogus deadline."

"We can do budget resolutions, and budget reconciliation, at any point. We can do it after Sept. 30," he said.

The Senate parliamentarian has determined that the current rules expire at the end of the month.

If Republicans wanted to pass ObamaCare repeal by a simple majority after September, they would need to include rules setting up health care in the fiscal 2018 budget resolution that is already being used to pave the way for tax reform.