But I think all of them would be in favor of a reform.

Almost everyone is in favor of a reform. But there is almost no specific package of reform that most people are in favor of.

Consider workplace enforcement. Most immigrant advocates and their allies in the Democratic base would denounce any such efforts, due to the effect that it would have on immigrant communities. If workplace enforcement is effective, undocumented immigrants would either be unable to work (inflicting penury and poverty on their households and their communities) or forced to work in far more precarious positions in the very underground economy.

You can see it now in NYC and Chicago. The problem isn't primarily that there are several tens of thousands of people moving there - it's that there are many people moving there that cannot legally work. That's straining their support and welfare systems to bursting. They can't handle that many people who depend entirely on the government for all their needs - especially housing. If you drove every undocumented migrant out of the workplace, you'd devastate entire communities.

Republicans want stricter enforcement, but are not willing to accept the level of legalization and permissive treatment of migrants already in America that the Democrats would insist on. Democrats want that legalization and path to citizenship - but are unwilling to accept the level of border security and workplace inspections that the Republicans would insist on. And for people that are in the mushy middle of immigration, they wouldn't accept either the GOP proposal (mostly enforcement) or the Democratic proposal (mostly legalization) - the status quo, which combines a mix of both, is preferable. For all sides, the current "no deal" is better than the best deal they could plausibly get from any other party.

Hence, the "no deal" wins.