Python: Limiting the size of a json string for posting to a server

I'm posting hundreds of thousands of JSON records to a server that has a MAX data upload limit of 1MB. My records can be of very variable size, from as little as a few hundred bytes, to a few hundred thousand.

def checkSize(payload):
    return len(payload) >= bytesPerMB 


toSend = []
for row in rows:
    toSend.append(row)
    postData = json.dumps(toSend)
    tooBig = tooBig or checkSize()
    if tooBig:
          sendToServer(postData)

Which then posts to the server. It currently works, but the constant dumping of toSend to a jsonified string seems really heavy and almost 100% too much, although I can't seem to find a way to do it another. Would I be ok with stringifying the individual new records and keeping a tally of what they would be together?

I'm sure there must be a cleaner way of doing this, but I just don't know.

Thanks for any and all help given.

This is the answer I'm now using, I came up with it at the same time as @rsegal below, just posting for clarity and completion (sendToServer is just a dummy function to show things are working correctly),

import pickle
import json

f = open("userProfiles")
rows = pickle.load(f)
f.close()

bytesPerMB = 1024 * 1024
comma = ","
appendSize = len(comma)

def sendToServer(obj):
    #send to server
    pass

def checkSize(numBytes):
    return numBytes >= bytesPerMB

def jsonDump(obj):
    return json.dumps(obj, separators=(comma, ":"))

leftover = []
numRows = len(rows)
rowsSent = 0

while len(rows) > 0:
    toSend = leftover[:]
    toSendSize = len( jsonDump(toSend) )
    leftover = []
    first = len(toSend) == 0

    while True:
        try:
            row = rows.pop()
        except IndexError:
            break

        rowSize = len( jsonDump(row) ) + (0 if first else appendSize)
        first = False

        if checkSize(toSendSize + rowSize):
            leftover.append(row)
            break

        toSend.append(row)
        toSendSize += rowSize

    rowsSent += len(toSend)
    postData = jsonDump(toSend)
    print "assuming to send '{0}' bytes, actual size '{1}'. rows sent {2}, total {3}".format(toSendSize, len(postData), rowsSent, numRows)
    sendToServer(postData)