Amazon API Gateway provides usage plans with quotas that can be used to limit the number of requests to your API. Quotas are enforced on a per-customer basis so a quota of 10K/month will allow 10K requests from a single customer/consumer of your API. This is the proper design for most real-world API projects.
But what if you’re building small-scale projects or personal projects where the cost incurred to you by your API in your AWS account is the biggest concern. What if you have a hard spending limit for API Gateway in your AWS account & you’re OK with shutting down the API for everyone as soon as the spending limit is reached. This can be achieved by creating an AWS Budget as shown below.
Start by visiting https://console.aws.amazon.com/billing/home?#/budgets & click Create a Budget:

In the next screen, set a budget amount & a filter for API Gateway:

In the next screen, set an alert threshold & provide an SNS topic that AWS Budgets can publish to:

Finish creating the budget, head on over to the SNS topic you provided above & create an AWS Lambda subscription to the topic. The Lambda function can then go & disable the API by zeroing out the method throttling limits of the API’s stage, as shown below:

This can be done using the AWS SDK & programming language of your choice or if you prefer to use the AWS CLI from a Lambda function to do the same, create a Bash Lambda as described here & use the following AWS CLI command in it:
aws apigateway update-stage \
--rest-api-id rxb7jktrj6 \
--stage-name my-stage \
--patch-operations \
'op=replace,path=/*/*/throttling/rateLimit,value=0'
aws apigateway update-stage \
--rest-api-id rxb7jktrj6 \
--stage-name my-stage \
--patch-operations \
'op=replace,path=/*/*/throttling/burstLimit,value=0'
Similarly, you can also create & schedule another Lambda function to be run on the first day of every month that resets the throttles so everyone can use the APIs again.