With both guaranteed top Shadow Cabinet jobs after Mr Smith becomes leader on 18 July, their election to the NEC would produce unprecedentedly close ties between the party's parliamentary leadership and the national executive.
Backers of their campaign argue it would help to ensure that Labour spoke with one voice. Even under the discipline of Neil Kinnock's leadership, the NEC, at times, sung a different tune to that of the Shadow Cabinet.
Assuming no surprises in the leadership, Shadow Cabinet and NEC elections, and should they be elected, the top five members of the Shadow Cabinet from Mr Smith down would also sit on the NEC. Aside from Mr Smith, Mrs Beckett, Mr Blair and Mr Brown, Robin Cook, Mr Smith's campaign manager, is already there and thought certain of re-election, while he is tipped as a likely trade and industry spokesman if he cannot have the shadow chancellorship. Mr Kinnock is thought to be certain of election to the NEC, ensuring a loyal phalanx for Mr Smith.
Both Mr Brown and Mr Blair - to the dismay of some MPs - stood aside in the leadership election and both have backed the Smith/Beckett ticket. Both, partly in public but mostly in private, have argued that Labour needs radical modernisation to win again - a tactic that has helped appease the more extreme modernisers, while Mr Smith has presented a safe face to more conservative elements.
Both Mr Brown and Mr Blair want to see Labour's constitution revamped, with a bigger party membership having a bigger say in policy, and with power devolved from Labour's Walworth Road headquarters to the regional structure and constituencies.
Their decision to stand does not guarantee their election. Some argued last night that the fact both were standing might dilute their respective chances.
Together with Mr Kinnock's decision to stand, the entry of three big names presages a tough fight for the seven constituency section places - and may threaten Bryan Gould's place.
While Gerald Kaufman is standing down, the next two to poll the lowest votes last year were Tony Benn and Mr Gould.
John Major told his backbench MPs last night that he was 'delighted' at the prospect of the Smith/Beckett 'dream ticket' after the Kinnock/Hattersley one, saying: 'We have a greater opportunity than ever before to knock Labour out of the ring for good.'
Labour's chief whip, Derek Foster, last night retained the post, easily surviving, by 158 votes to 90, a challenge from John Evans, the Labour Party chairman.Reuse content