This claim has some truth weaved into its misleading information. 
Yes, it is an undeniable fact that government employees, including those who work for the VA. USA Today equates it to roughly 15,000 however; Half of what the claim suggests. The only evidence suggesting upwards of 30,000 losing their pay is only based in the words of VA secretary Doug A. Collins, a known Trump loyalist, and a man who also bases this on the fault of the democrats.
The most important pieces of information to understand when trying to make sense of the government shutdown boils down to two major factors; what the original dispute in legislation was over, and who holds more power within the chambers.
As with any government shutdown, the root cause stems from the various chambers not being able to pass the budgeting bill for the government by its deadline, due to disagreements on where money is to be allocated. This shutdown in particular had a major dispute over healthcare spending. Democrats want to push programs to drop healthcare premiums for millions Americans, while widening the scope of access to health services to citizens. Republicans refuse to include this in the bill. Reputable sources such as NPR, the BBC, and Harvard Kennedy School all state this to be the case. 
According to these sources, In terms of who holds power, republicans control both chambers of Congress, but are 60 votes short of passing the bill in the Senate. This allows for a small gap of wiggle room available to the democrats. 
In actuality, this is a GOP shutdown. The party in power often has the ability to negotiate and appease the other side while leveraging the deal to still further their own goals. That is the logic of compromise that the US Government supposedly holds within its framework. Yet, the Republicans refuses to even budge, even though the democrats push a problem that should ideally be bi-partisan. 
As unfortunate as the shutdown and lack of pay is, the problem is simply more nuanced than pinning the blame of the party in opposition to the governing party and calling it a day.