McConnell’s comment came after the administration decided to delay until 2015 a requirement that employers with more than 50 full-time employees provide health insurance. 

“We knew ObamaCare would be unaffordable, but now we also know it will be unfair,” Sen. Mike LeeMike LeeThis week: GOP picks up the pieces after healthcare defeat Lawmakers signal fight for healthcare reform is not over Lee: Healthcare 'absolutely not' behind us MORE (R-Utah) said ahead of McConnell. “It is unfair to protect the bottom lines of big businesses while making hard working families pay stiff penalties.”

This week, the House will vote to delay that mandate just as the administration proposed. But the House will also vote to delay the healthcare mandate for individuals. Republicans argue that Obama shouldn’t be able to pick and chose which parts of the Affordable Care Act, also known as ObamaCare, to follow.

“American families also deserve relief,” Lee said. “Republicans in Congress must now stand up for the individuals and families who do not have the lobbyist that big businesses do to get the administration’s attention.”

Obama threatened to veto both of the House bills if they made it to his desk. Sen. John CornynJohn CornynThis week: GOP picks up the pieces after healthcare defeat GOP senators pitch alternatives after House pulls ObamaCare repeal bill Rand Paul takes victory lap on GOP health bill MORE (R-Texas) said he couldn’t see why Obama would veto a bill that does the same thing his administration is doing unless he wanted to “unilaterally” decide which laws to follow.

“If this president or any president is allowed to pick and chose which laws to follow for the sake of expediency, then we have lost constitutional power,” Cornyn said. “The president is showing disdain for those checks and balances.”

McConnell and Cornyn said instead of delaying aspects of ObamaCare, the law should be fully repealed.

“It’s an important first step to giving all Americans and all businesses what they really need: which is not a temporary delay for some, but a permanent delay for everyone under this law,” McConnell said. “The politicians pushing ObamaCare might not like that. But they’re not the ones who are going to have to live with this thing the same way most Americans will.”

Republicans have argued that the healthcare law will harm the economy and increase healthcare costs and taxes on the public. Democrats point to benefits of the law that have already gone into effect for people younger than 26 who can stay of their parents’ insurance plan, people with preexisting conditions that can’t be denied coverage and women who no longer have to pay for preventative care.