If you are thinking of holding the work hostage until you get a raise, then it is possible they would give you the raise to get the work out but would immediately fire you afterwards. That is a totally unacceptable way to behave.
You agreed to your current salary. You were assigned to do the work. You have an obligation to deliver it.
Holding your manager hostage for a raise by ensuring the failure of a project is one of the worst possible actions you can take. You change from someone who has helped us overcome great obstacles and who has delived something of value to the business and who may deserve to be rewarded for that to someone who is unreliable and who will stop progress every time he is not happy about something. That is the kind of person most companies do not want to continue to employ. And the kind of person they tell their friends at other companies about so that no one wants him after he is fired.
At work there will be plenty of times when you are not completely happy with everything. You can't just decide not to do yourj ob because of that.
The last time I asked for a raise it took 4 months of negotiations not three weeks as they had to find the money in a tight budget and get approvals from many different people. And that was when everyone along the line was in agreement about actually giving the raise and there was no one who had to be convinced that I deserved it. The work world doesn't always move as quickly as we would like. Sometimes approvers are on vacation and somtimes they are busy with other things and take their time to get to the request. Sometimes a new company may not even have a process set up to know who has to approve. There are other things that affect a choice to give a raise and other roadblocks that need to be cleared. The money has to come from somewhere and sometimes when money is tight, it is hard to find.
I don't know if they will give you the raise you want. They may say yes and they may say no. You may have to be prepared to move on to another job that places more value on what you bring to the table. However at no time should you try to force a raise through failure to do your job.
As far as the verbal agreement, I guess you should consider this a lesson learned. Never rely on a verbal agreement for a monetary reward.