"deeply nervous" is correct and usable in written English.
You can use it to describe a feeling of intense anxiety or fear. For example, "John was deeply nervous before he had to give his speech in front of the large audience."
But some environmental groups are deeply nervous.
Now that he was watching, he seemed deeply nervous.
His victory deprived Mr. Obama of his 60-vote supermajority and left Democrats deeply nervous.
It got to the stage that Adams became deeply nervous about sending out any kind of email communication.
When she reached a customs agent as she crossed into Canada, she recalled, she felt deeply nervous but also relieved.
A deeply nervous White House knows that defeat today for the Democrat candidate in Massachusetts today would be seen as a searing repudiation of all that Mr Obama has done – or failed to do – in the 12 months since his inauguration one year ago tomorrow.
I was allowed to go to his funeral, but vomited all over the prison van—I had not driven anywhere in a few years, and I was deeply frustrated, nervous, and sad.
All I know is the wannabe Soldiers of Odin I've met made me deeply uncomfortable and nervous.
They have to realise that the IRA's armed struggle is over.' Several of Trimble's closest allies were nervous and deeply uncertain about the IRA plan to put arms beyond use and allow international observers to monitor arms dumps.
She creates a sincere young woman who is painfully eager to please, bristling with nervous energy, deeply insecure about her looks and even her voice long after she has become a star.
Apatow She was deeply upset, because she was nervous about doing it.
