If the Republicans want to look a bit more politic, here are two conditions to tie to Ukraine funding.

Regarding asylum and border security:

Asylum
Claims for asylum can only be made
1. By those who have lawfully entered and remain in the United States
2. At any US embassy or consulate abroad
3. Via the CBPOne app outside the United States

That's it. It's easy to explain and does not require a 320 page bill or a week of analyst time to digest. The public will understand what it means, and it is fundamentally reasonable. It will not stop illegal immigration in its totality, but should reduce undocumented entry to more customary levels of border chaos.

I might add another condition:

The Ukraine Compensation Fund
The President shall endeavor to redirect the Urals Discount to a G7 Entity to be used for funding military and economic assistance to Ukraine.

If the point is to reduce the fiscal burden of the war on the US, then the most tangible source of funds is the Urals discount, the difference between Brent and Urals, Russia's western oil export price. That's worth about $34 bn / year based on today's oil prices, and could be worth twice that next year if oil fundamentals develop as many in the industry expect. Should this be successfully implemented, our analysis suggests the Russians will have effectively lost the war.