The two senators from Kansas objected to Reid's "un-American" comment.
Rand Paul's legislation would apply to all laws a president tries to not enforce as written.
The Senate voted 97-0 Thursday to confirm Michael Connor to be deputy secretary of the Interior.
Connor will serve under Secretary Sally Jewell.
Republicans said the new healthcare and education programs was not properly paid for.
Sen. Roy Blunt (R-Mo.) countered Senate Majority Leader Harry Reid's (D-Nev.) remarks that all of the ObamaCare “horror stories” are lies, saying, “they are not all untrue.”
Blunt was responding to remarks Reid made on the Senate floor Wednesday. Reid said the “horror stories” told in anti-ObamaCare ads are “all lies.”
Senate Minority Leader Mitch McConnell (R-Ky.) demanded Thursday that the Internal Revenue Service (IRS) not impose a rule denying tax-exempt status to political groups.
“Left, Right, or Center — folks understand what a threat this rule poses to our most cherished of civil liberties,” McConnell said on the Senate floor.
Senate Majority Leader Harry Reid (D-Nev.) said Thursday that Republicans injected politics into a veterans bill that should have been bipartisan.
“Shame on Republicans for bringing base-politics into a bill to help veterans,” Reid said on the Senate floor. “They are pushing an unrelated amendment on Iran that they knew would kill the bill.”
Reid's move comes as the two parties fight over amendments.
“I guess if you make that much money, you can make these immoral decisions,” Reid said.
After several Republicans bashed President Obama’s recent plan to cut subsidies to Medicare Advantage, Sen. Chris Murphy (D-Conn.) defended the decision Wednesday.
Under the Affordable Care Act, also known as ObamaCare, the federal government is using savings from cuts to Medicare Advantage, a private health insurance alternative for seniors, to help reduce the cost of prescription drugs for seniors.