With Republican Sen. Rand Paul getting on board Tuesday morning  the immigration reform train is speeding up.

Now, a half-dozen Republican senators want to slow it down.

Sen. Charles Grassley (Iowa), the ranking Republican, and Chairman Patrick Leahy (D-Vermont) sit on the Senate Judiciary Committee. (Chip Somodevilla/Getty Images)

The lawmakers, all members of the Senate Judiciary Committee, sent a letter to Chairman Patrick Leahy (D-Vermont) asking him to allow more time for hearings on a comprehensive immigration bill before scheduling a committee vote. A bipartisan Senate group is drafting a bill that it plans to unveil in April and that is expected to be the template for a possible agreement between Congress and the White House.

“The last time Congress considered legislation of this magnitude that was written behind closed doors and passed with no process, it resulted in sweeping changes to our healthcare system, the negative consequences of which are only now coming to light,” the Republicans wrote to Leahy. “If we bring these important issues to the Senate floor without them having been worked through committee, it is a prescription for a real problem.”

The letter was signed by Sens. Charles Grassley (Iowa), the ranking Republican on the panel; Orrin Hatch (Utah); Jeff Sessions (Alabama); Mike Lee (Utah); and John Cornyn and Ted Cruz of Texas. A Judiciary Committee staff member confirmed that Leahy’s office received the letter but that he was on the Senate floor talking about the continuing resolution spending bill and had not yet reviewed the letter.

In the letter, the senators said the Judiciary Committee has held one hearing on comprehensive immigration reform Feb. 13 and two hearing this month on components of the immigration system, including the effect of immigration laws on women.

Leahy said early mid-January that immigration would be the committee’s top priority after dealing with gun violence-related bills. In the February immigration hearing, Homeland Security Secretary Janet Napolitano testified and committee members also asked Attorney General Eric Holder questions during a separate hearing, according to committee staff.

“We believe that hearings are necessary to examine implementation of the components essential to a workable system,” the GOP senators wrote, “especially given that 43 current members of the Senate were not here during the last debate in 2007.”