The phrase "almost impossible to support" is correct and usable in written English.
You can use it when discussing a situation, idea, or argument that is very difficult to justify or back up with evidence.
Example: "The theory presented in the paper is almost impossible to support with the current data available."
Alternatives: "nearly unfeasible to justify" or "hardly possible to back up".
For Americans, Jewish or not, who identify with Israel but oppose the occupation, the collapse of the peace process makes it almost impossible to separate supporting Israel from supporting the religious-nationalist zealots of the settler movement.
Without my physicians' support, it was almost impossible to find support from others.
This means projects find it almost impossible to squeeze support, ultimately more important, out of the money available.
If their marriage breaks down or her husband dies, women have little recourse as it becomes almost impossible to seek spousal support and even child support.
Considering the specialization of biological databases, even many of the big ones do not have this volume of traffic, and therefore attracting commercial clients makes it almost impossible to raise enough revenue to support BRCs.
But the more important explanation is that single life is generally more insecure and chaotic than married life, and single life with children — which is now commonplace for women under 30 — is almost impossible to navigate without the support the welfare state provides.
Syria: Through a series of events almost impossible to sort out, having essentially supported the Arab Spring nowhere else, the Obama administration chose to do so in Syria, attempting to use it to turn President Bashar al-Assad out of office.
The environment makes it almost impossible to get essential evidence, necessary support and proper legal advice.
Gates has denied he is trying to silence McChrystal, but it is clear the administration is fearful of being pushed into deeper involvement in a war from which it might prove almost impossible to extricate itself while public support for fighting in Afghanistan continues to decline.
While most Arabs are horrified by Assad's treatment to Syrian people, it is almost impossible to find any kind of support for U.S. intervention.
