Sen. Ted Cruz Rafael (Ted) Edward CruzLoeffler calls for hearing in wake of Netflix's 'Cuties' Health care in the crosshairs with new Trump Supreme Court list 'Parks and Rec' cast members hosting special reunion to raise money for Wisconsin Democrats MORE (R-Texas) acknowledged on Saturday that Senate Republicans face an uphill battle to pass an ObamaCare repeal bill, warning that a failure to do so would be "catastrophic."

"For seven years the Republicans have been promising, 'If only you elect us, we’ll repeal ObamaCare,' " Cruz told conservative radio host Larry Kudlow.

"I think the consequences of failure would be catastrophic. But it’s going to take senators across the Republican conference being willing to sit down in good faith."

The GOP's narrow majority in the Senate, Cruz said, would make coming to an agreement on healthcare reform a "difficult task." He noted that a slew of obstacles ranging from the ideological to the geographical could pose challenges.

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The House on Thursday narrowly passed an amended version of the American Health Care Act (AHCA), a measure that repeals key elements of ObamaCare.

GOP lawmakers have long vowed to repeal former President Obama's signature healthcare law, and with a unified Republican government saw an opportunity to make good on that promise.

But the first version of AHCA was pulled from House consideration in March amid dwindling support among Republicans. Conservatives argued that the bill did not go far enough to repeal certain provisions of ObamaCare, while moderate Republicans voiced concern that the measure could lead to massive losses in coverage.

The amended version of the bill attempted to address those concerns. It would allow states to waive ObamaCare's rule prohibiting insurers from charging people with pre-existing conditions more for coverage, while providing $8 billion over five years to help those individuals.

But the House vote was only the first victory for the measure, and it is likely to face intense scrutiny in the Senate, where some Republicans have indicated that they will vote on their own healthcare reform bill.

"In the Senate we have a difficult task ahead of us," Cruz said. "We have a very narrow majority. We have just 52 Republicans — hold at least 50 of those 52 Republicans to pass the bill."