I hate to get sucked into this sort of political bickering here, but I feel like you're being a bit disingenuous. Yes, democrats during the Obama years did hold out for comprehensive reform, but to their credit it looked like they were only a few votes short for several years so their strategy made some sense. Additionally, it was the strategy of the Republicans in the House and Senate at the time to float small one off reform bills on various topics in order to peel votes off of broader initiatives and then scrap the smaller bills once the broad reform was killed.
You do have some Republicans who have some interesting things to say on immigration like Justin Amosh, but he's an exception. The nativists in the Republican party have been increasing in power an influence since 2010, and they want less overall immigration even among high skilled immigrants, it's literally part of their platform.
I would personally be in favor of scrapping the current system totally and setting a single cap per year. I would also give special consideration to refugees and skilled/in demand workers. I think increasing the number of temporary work visas is probably good as well. Now we have a cap per country, which is ridiculous.