Reid has said he will bring to the floor a bill to expand background checks, reduce interstate gun trafficking and improve school safety. He's also expected to allow amendments to add limits to high-capacity magazines, a ban on assault weapons and heightened mental health screening.
Lee, Paul and Cruz say they will hold up any effort to do so.
"The Second Amendment to the Constitution protects citizens' right to self-defense," the senators say in their letter. "It speaks to history's lesson that government cannot be in all places at all times, and history's warning about the oppression of a government that tries."
Reid's communications director, Adam Jentleson, said that while the move by Lee, Paul and Cruz isn't surprising, "It's outrageous that these senators are unwilling to even engage in a debate over gun violence in America."
"No matter your opinion on this issue," Jentleson continued, "we should all be able to agree with President [Barack] Obama when he said that the children and teachers of Newtown, along with all other Americans who have been victims of gun violence, at least deserve a vote."
White House press secretary Jay Carney said it would be unfortunate if the senators do indeed try to block the legislation and votes on the critical issue.
"I don't think you need to tell the families of those who have lost their children to gun violence that bills like this might be filibustered I don't think that would be welcome news," Carney said.
Sen. Dianne Feinstein, D-Calif., is expected to bring up her bill to reinstate the assault-weapons ban as an amendment to the Reid bill.
The measures come in the wake of high-profile shootings, including the massacre at Sandy Hook Elementary in Newtown, Conn., that left 26 children and adults dead.