Moderate DEM Hold
This race seems to be a a fairly reasonable bet that Shaheen will win re-election, albeit by single digits. While the PVI for the state is only D+1, it has been trending blue as of late. (particularly in recent statewide elections) At the very least, it would be fairly easy for Shaheen to portray Brown as an opportunistic carpet bagger looking for a door back into the Senate after losing re-election.
There has yet to be a single poll showing Brown in the lead. The current RCP average for the race is Shaheen +5. The only poll to show her not in the lead is a Purple Strategies poll back in January which shows a 44%-44% tie. The polls this month for this race show:
49%-43% Shaheen (CEA/Hickman Analytics (D))
39%-36% Shaheen (Dartmouth)
45%-39% Shaheen (WMUR/UNH)
The only deviation in this race seems to be her margin of victory rather than a different victor. Unless there is some large Republican wave or a disaster in the Shaheen camp, this race will stay blue in November.