They can:
1) Lobby other states' representatives and senators to get legislation moving.
2) Vote out their existing representatives and replace them with ones who are more sympathetic to that issue.
3) Bring a lawsuit in federal court.
Things like that.
The states can't take unconstitutional actions because they feel the feds aren't doing their job.
Immigration is hardly the only issue with federal responsibility and federal inaction over the last couple of decades...
Cheers,
Scott.