I apologise, I think I have misunderstood the issue. Are you saying the following?
That SRX1 ge-0/0/0 1.1.1.1/30 is connected to SRX2 ge-0/0/0 1.1.1.2/30.
SRX1 can not ping 1.1.1.2.
If so then please double check the following:
Cable plugged into the correct port.
IP address configured correctly on the correct interface, and in this case with no VLAN tagging.
The interface on both SRXs are within a security zone.
The security zone allows icmp as a host inbound service.
There is no firewall filter on the interface or on the control plane (loopback interface) to block ICMP from the source address.
Can you ping your local interface i.e. SRX1 can ping 1.1.1.1 and SRX2 can ping 1.1.1.2.
If none of this helps then please attach entire configs of both SRX devices and myself or someone could take a look.