The Strengthening and Enhancing Cybersecurity by Using Research, Education, Information, and Technology (SECURE IT) Act, according to McCain's website, would promote collaboration between government and private industry, update existing criminal laws to reflect the digital revolution and enhance "research programs to protect critical networks."

"This legislation will help us begin to meet the very real threat of cyberattack," said McCain on Thursday. 

Meanwhile Senate Majority Leader Harry ReidHarry Mason ReidMcConnell not yet ready to change rules for Trump nominees The Hill's Morning Report — Sponsored by CVS Health — Trump’s love-hate relationship with the Senate Trump to press GOP on changing Senate rules MORE (D-Nev.), who in practice controls the floor schedule, offered a positive sign for the legislation, saying he would at least look at it to be part of larger package of legislation.

"I look forward to a debate on the Senate floor that will ensure this bill and other proposals get a fair hearing, and which will allow thorough consideration of amendments to improve the legislation," he said in a statement released Thursday.

The Senate floor has remained quiet for most of Thursday afternoon.