Not with built-in JSON.parse. You'll need to parse it manually and treat values as string (if you want to do arithmetics with them there is bignumber.js) You can use Douglas Crockford JSON.js library as a base for your parser.
EDIT2 ( 7 years after original answer ) - it might soon be possible to solve this using standard JSON api. Have a look at this TC39 proposal to add access to source string to a reviver function - https://github.com/tc39/proposal-json-parse-with-source
EDIT1: I created a package for you :)
var JSONbig = require('json-bigint');
var json = '{ "value" : 9223372036854775807, "v2": 123 }';
console.log('Input:', json);
console.log('');
console.log('node.js bult-in JSON:')
var r = JSON.parse(json);
console.log('JSON.parse(input).value : ', r.value.toString());
console.log('JSON.stringify(JSON.parse(input)):', JSON.stringify(r));
console.log('
big number JSON:');
var r1 = JSONbig.parse(json);
console.log('JSON.parse(input).value : ', r1.value.toString());
console.log('JSON.stringify(JSON.parse(input)):', JSONbig.stringify(r1));
Output:
Input: { "value" : 9223372036854775807, "v2": 123 }
node.js bult-in JSON:
JSON.parse(input).value : 9223372036854776000
JSON.stringify(JSON.parse(input)): {"value":9223372036854776000,"v2":123}
big number JSON:
JSON.parse(input).value : 9223372036854775807
JSON.stringify(JSON.parse(input)): {"value":9223372036854775807,"v2":123}
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