Compare the amnesty deal under Reagan, where the democrats broke their word immediately, dealing the Republicans a long-term, serious injury that they are still trying to recover from to this day.

Reagan personally issued an executive order legalizing even more illegal immigrants than the law had covered. Bush Junior ran on a very pro-immigration platform, and during the 2000 debates as far as I can tell the issue never came up once (searching Ctrl+F for "immigr" or "border security" turns up nothing in these transcripts). Also, the Republicans held the Presidency for 15 out of 23 years from 1986 to 2008, after which illegal immigration became net-negative and has been net-negative ever since, yet somehow there was never much effort to enforce the laws against employing illegal immigrants.

Heck, even Trump has conspicuously failed to put serious effort into enforcing the laws against employing illegal immigrants, though his administration has put plenty of effort into preventing the entry of economically unproductive refugees and building a border wall of dubious utility.

If there was a deal back then, I highly doubt that either party was serious about it.