I have a work project due tomorrow. I've been really busy recently.
I've been really busy recently due to a work project that's due tomorrow.
"I have a work project due tomorrow. I've been really busy recently."
I assume you mean you have a work-based task that was due so it is best to use the phrase "work project"as this is more commonly used in English.
"I've been really busy recently due to a work project that's due tomorrow."
The other way to state this is to mention that you've been busy first and the expand on to the reason why afterwards
"I have a work project due tomorrow. I've been really busy recently."（明日が納期の仕事があって、最近すごく忙しかったです）
= 締め切りを迎える仕事の課題があるということだと思います。それなら、"work project" というフレーズを使うのがベストです。英語でよく使われます。
"I've been really busy recently due to a work project that's due tomorrow."（明日が納期の仕事があって、最近すごく忙しかったです）
= まず忙しかったと伝えて、それからその理由を説明することもできます。
I have a work project due tomoroow so I have been really busy recently
I've been really busy doing a project that's due tomorrow
If you want to say you have not had much time as you have been working then this is said to be 'busy' or 'really busy' when explaining something that has happened not that long ago this is called 'recently'
If something needs to be taken or handed in then it is said to be 'due' then
I had a deadline for tomorrow so I was really busy.
I was really busy seeing that I had work due tomorrow.
Sorry I was unavailable, I had some work due for tomorrow that I needed to complete.
Seeing that: because
Unavailable: unreachable
Complete: finish
Due: required
Deadline: finishing time/due
When we have a deadline we have little time to do anything else until we are done with the work.
We can use the above sentences to express the idea that we were busy with completing work.
I've got a deadline tomorrow so have been rather busy recently
I've been pretty snowed under recently as I've got a deadline to meet tomorrow
If you have a job due to be completed tomorrow and have been busy recently - and wish to express that, then one of the above expressions should do.
If you are SNOWED UNDER, you have been struggling to complete all the necessary work you have.
I have an assignment due in tomorrow so I've been busy
I've been busy with work due tomorrow
I have a work deadline tomorrow so I've been busy with that
It's a very common expression to say you have a 'deadline' or saying something is 'due' for a date when talking about work or studying. There are many ways you could say 'job' such as 'task', 'assignment', 'project' or 'role'.
Other expressions include:
'I was really busy since I have a work assignment due tomorrow'
'I've been busy working on an assignment that is due tomorrow'
deadline' や 'due' は、仕事や勉強について、よく使われます。
'job'（仕事）の言い方はたくさんあります。
例えば：
'task' 'assignment' 'project' または 'role'
次のように言うこともできます。
'I was really busy since I have a work assignment due tomorrow'
（明日締め切りの仕事があってすごく忙しかったんです）
'I've been busy working on an assignment that is due tomorrow'
（明日締め切りの仕事があって忙しかったんです）
アメリカ合衆国 
日本 
イギリス 
南アフリカ 
