Republicans at both ends of the conservative spectrum took issue with the bill for different reasons.
Mr Trump chided lawmakers as the Senate reconvened after a week off for the July 4 independence holiday and with the House of Representatives scheduled back in session on Tuesday.
The demonstrations started in the afternoon, and police were called to 13 locations inside the compound in response to calls.
It remains to be seen whether the new bill will be able to bridge the divide.
McConnell also announced Tuesday that the Senate will delay its August recess by two weeks amid a packed legislative agenda.
Trump said congressional Republicans' votes to repeal the Affordable Care Act during the Obama administration "didn't mean anything", undercutting Republicans' frequent boasts that the symbolic repeal votes showed their resolve to get rid of the legislation.
The U.S. House included the tax break for insurers in its version of the bill that passed in May.
"I also know that if we want health care in rural places and across Kansas, Medicare and Medicaid need to compensate for the services they provide". However, before that they proposed for a bipartisan deal which would help with the payment of the insurance subsidies to a "repeal and delay" plan. But said the challenge is how much that costs, indicating senators are waiting for the CBO to give an assessment of the amendment. It's out of business and we have to get this done. Yet even he is having trouble supporting the GOP bill.
Trump and his spokespeople have said positions have been left vacant to trim the size of the federal government.
The roughly 14 million American families earning $200,000 or more would enjoy an annual net benefit of roughly $5,400 a year by 2026, when the law would be fully implemented, the study found.