An air carrier crew unsuccessfully requested several weather deviations and were then asked to squawk 7700. The crew did squawk 7700 but did not declare an emergency. They were given an altitude change in order to regain separation.

Narrative

At FL340 had a solid line of thunderstorms east of us that angled to our 1 o'clock position. It required a right deviation which I requested from Center. The Controller gave us a clearance to deviate left and descend to FL300. I told her we could not accept a left deviation. A few minutes passed and the First Officer called to request a right deviation. She replied negative; to which I responded we could not continue on our present course or deviate left. I called a third time requesting a right deviation and told her we needed to turn 10-15 degrees right. She cleared us to deviate and asked us to squawk emergency. A minute or two later she asked if we could change altitudes and we answered yes. She gave us a descent to FL300 and cleared us direct to a VOR; which was a larger turn to the right. After a few minutes she had us return to our original squawk. We did not declare an emergency. The rest of the flight was uneventful; and as we left the frequency; she thanked us for our help. I found the squawk emergency request very unusual. My assumption is that the squawk allowed her to get relief from separation requirements. We had no traffic indication on TCAS. I just want to document the event; as I have never had an ATC request to squawk 7700. To our knowledge; we did not deviate from a clearance; and no loss of traffic separation occurred.