Sen. Bill Cassidy (R-La.) on Sunday urged his colleagues not to mix healthcare reform and tax reform while pushing an alternative healthcare bill that he co-authored.

"Let's first talk, Chris, about why they've had such a problem passing any plan. They are trying to combine tax reform with healthcare reform," Cassidy told host Chris Wallace on "Fox News Sunday." "Don't mix the two. We don't mix the two."

Cassidy, a former doctor turned lawmaker, has proposed his own bill with Sen. Susan Collins Susan Margaret CollinsSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (R-Maine). Both Republican lawmakers have expressed reservations with the Senate bill to repeal and replace key provisions of ObamaCare.

Cassidy on Sunday expressed doubt that President Trump can keep his key campaign promises to "cover all, care for pre-existing conditions, eliminate the individual and employer mandate, and lower premiums."

Cassidy touted his bill as the key to making sure all those pledges are kept.

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"If we are serious, Cassidy-Collins is the only way to get there," Cassidy told Wallace, adding that six other senators are on board with their plan.

"Healthcare is like no other issue. It touches people in their most personal being. That is why we got to get it right," he added.

Several GOP lawmakers have spoken out against the Senate GOP's bill, while others remain undecided.

Opposition to the bill led Senate GOP leaders to delay voting on the measure until after the July Fourth recess.

While Republicans have 52 seats in the upper chamber and enjoy majority power, Republicans can only afford two defections to pass the bill with Vice President Pence casting a tie-breaking vote.