"We have had - for seven years - we have promised to do that", he told an audience at the Renaissance Austin Hotel.
Instead, Republicans have run in different directions, proposing everything from a bipartisan deal to pay for insurance subsidies to a "repeal and delay" plan that would give them a few years before the Affordable Care Act would be fully gutted.
Yet Mr. Trump - who has been all over the map on this issue - lauding the House bill one day, calling it "mean" just days later, doubled down on his wild assertion that this would be "so easy" to do.
We would especially like to talk with you about our concerns with the new Senate health care bill.
Facing few good options, Mr. McConnell last week signaled that Congress will have to patch up Obamacare's ailing markets if Republicans can not smooth over their differences and pass a replacement plan.
"I was wondering with the new health care law coming out, will it impact veterans at all?" one audience member asked. Ben Sasse, R-Neb., suggested that Republicans could repeal most of the ACA, forcing Democrats to the table to work on a replacement. Cruz's amendment could be a pathway to gaining the support of conservative lawmakers seeking to lower the cost of premiums.
So as they head back to the swamp of Washington, D.C., Senate Republicans face a ideal storm: No clear path for a bill, a short timeline to get it done, and a full plate of other priorities to accomplish before the same deadline.
Cruz said it is critical for Congress to focus on lowering premiums and to "honor our promise to repeal Obamacare - it isn't working and people are hurting across the state and across the country".
Republican leaders are now waiting for an updated estimate from the nonpartisan Congressional Budget Office on how tweaks to the first version of the bill would affect national coverage levels and federal spending.
"You, the consumer, should be able to choose what healthcare you want to buy", Cruz said on ABC's "This Week". And he said it's very important it does.
"I believe we can get to yes", said Cruz.
"I think that reopens an issue that I can't support, that it would make it too hard for people with preexisting conditions to get coverage", Sen.
"What we have found is there are people who are trying to come in from out of the district to disrupt town hall meetings and not have a civil discussion", Ryan said.
More than a dozen Austin groups demonstrated outside the hotel before Thursday's forum. He said he hasn't decided how he will vote on the Senate's health care bill because he wants to "judge the final product". Collins said the plan would lead to unaffordable costs for individuals with pre-existing conditions and caps on coverage.
As was the case at that Harrisburg rally, Casey was joined Monday by people who said they were helped by the Medicaid expansion authorized by the Affordable Care Act.