There is a myth about the Liberal Democrats that their main artery of support stems from the Labour Party, when in fact their appeal is as much to the Conservatives voters. If the Lib-Dems were to enter a progressive alliance many 'shy Conservatives', of whom vast amounts were Lib Dem voters who gave the conservatives their general election victory, would find it difficult to vote for an alliance with Labour in its current form. An alliance would in fact make a Conservative government more likely. The main way the Lib -Dems can help stop a Conservative government is by having a revival across the South in seats where they are in direct competition with the Conservatives.
The Lib -Dems got a bumper election results in 2010, not because of a mass appeal to Labour voters, but on how they appealed to Conservative voters. There were three factors that contributed to the Lib Dems electoral success and none of them could be said to be a traditional pitch to Labour voters in the public sector or amongst the working class. Firstly, Nick Clegg's charisma remember the TV Debates. Secondly, the tuition fees policy, which was a protest vote much like the Iraq War which mopped up votes, many Labour voters, especially the young, in areas such as Brent Central, which before the boundary changes in 2010 had been a safe Labour seat. (Bar Sarah Tether winning Brent East in 2003 in a by-election after the Iraq War). Finally, In 2010 they were offering tax cuts to the managerial and professional classes, which according to analysis make up the majority of Lib Dems . In their manifesto in 2010 they promised to "Cap pay rises at £400 for all public sector workers, initially for two years" and to introduce a Mansion Tax on properties worth more than two million, whereas Labour were planning on introducing rates on properties of more than 1 million. This tactic paid off for the Lib Dems . If you look at their top 30 targets seats for the 2010 general election , they gained three seats from the Conservatives compared to one from Labour.
In the overall tally at the 2010 general election the Lib Dems held 36 seats where the Conservatives were in second place, compared to 18 where Labour was. On top of this when you look at the Labour seats the Lib Dem held in 2010, the vast majority of them had since the post war period been relatively close races with the Conservatives, but since the early to late 1990's the Lib- Dems had been vying with the Conservatives for second place, an example of this is Leeds North West
The Conservatives won the 2015 general election because of the Liberal Democrats. Going into the general election the Lib Dems had 57 seats. All the Labour seats that the Lib Dems held bar one, went back into Labour hands, whereas the Liberals lost 27 seats to the Conservatives. The Conservatives could not have achieved a majority with the seats that they won from Labour. It was the Lib Dem voters that got them over the finishing line.
These 'shy conservatives' voters were not voting against the Coalition austerity otherwise they wouldn't have voted for the Tories. They are socially liberal but fiscally conservative. When they feel the Conservatives are not too nasty they float back to them.
They don't want an overtly left wing government in power. Just look at
Saatchi and Saatchi's campaign, with the image of Ed Miliband in Alex Salmonds pocket. Firstly, it played into the idea of nationalism and fears of the unions . Secondly, and more importantly, it insinuated that you would be getting a radical left wing government if you voted anything but Conservative. These are voters that not even Blair could win over in 1997 in constituencies such as Clochester, Portsmouth South and Eastleigh. Corbyn will not get anywhere close to these voters and if the Liberals were in an alliance with Labour it would likely increase the chances of these voters continuing their support for the Conservatives.
We are in one of the most unpredictable electoral cycles. The effect of Brexit could go in any which direction at the moment. Brexit may well attract shy Conservatives to the Liberals, we will have to wait for the result in Richmond.However, the idea of a progressive alliance between the Liberals and the Labour party would compound rather than erode the Conservatives lead. If the Liberals would enter an alliance it would likely haemorrhage their shy conservative support further into the hands of the Conservatives, as they will not want to vote for alliance that they will perceive to deliver a radical left wing approach to this country.