I believe the House stopped that bill, not the Senate.
Once again, the huge battle in the Senate that Cruz and Sessions led, alerted the public to the Gang of 8 bill. That was really the beginning of Cruz’s working relationship with House Conservatives. Boehner was on board with the cheap labor express until the public outcry and melting the phone lines to Congress applied enough pressure to stop the bill.
Both Rush and Levin credit Cruz with the defeat of the Gang of 8.
FYI. Cruz has been meeting with House conservatives at least since 2013. He met with them before over DACA (which involved alien children being brought into the US) PP defunding, and Obamacare defunding among others. The dems have been known to whine about it.