From your last statement how do you conclude giving amnesty as being supporting illegal immigration. If you want to understand what the Dems support then go back to the gang of 8 from 2013 bill they tried to pass which was a bipartisan effort. All the things you list were on that bill, increase border security, stricter enforcement on expired visas etc. The thing is it took 10 years to become a citizen for people seeking citizenship and there were a lot of rules that had to be followed in order to make it. There was no amnesty for all and the effort was to make it easier to find people who probably should be deported for people who are looking to become legal.
Giving a path to citizenship to illegal immigrants is supporting them lol. You're not punishing them for their crime but instead rewarding them.
You do know there is a huge service and agricultural industry that depends on these illegal immigrants. Why do you believe that ICE isn't heavily finding illegal immigrants in those industries. The reason is because it would nuke the country. ICE could easily hit every farm, hotels and other service industries that use illegal immigrants. How many Americans are lining up to work fields and pick fruit or working cleaning people homes etc.
The reason for giving the current people here amnesty and a path to citizenship is to bring those industries in line and have those people pay taxes instead of getting paid under the table. It would mean higher wages because those industries would not be able to pay dirt cheap prices for their labor and at least minimum wage. Giving amnesty also allows for working IDs in those industries making it harder for any new illegal immigrant to work in those industries leading to less illegal entry.
While you try to make it black and white, it really isn't. America has run on illegal immigration for a long time an benefited from the cheap labor that you probably did not know you enjoyed.