As a Virginian, the big effect might not be on 2012, but on Virginia in 2013 and 2014. I'd know, I'm not only Virginian, but I live in Cantor's district and attend his synagogue.
Cantor may be enough to flip Virginia red again - one of the key swing districts that determine who wins Virginia in Presidential races is HIS district, coincidentally, my district. Henrico County trends Republican, and turnout in other parts of the state are higher, Virginia flips. Romney still loses, but the race is much closer.
Where things get interesting is Virginia politics - 2013 was were the Virginia GOP really started falling apart. The reason they're borderline impotent at the state level these days can be traced to three things:
1) Losing the Governor's race in 2013 when Ken Cuccinelli forced the GOP nod to go to him instead of Bill Bolling. Bolling was popular enough the Dems ran Terry McAuliffe as a "sacrificial" candidate, the deeply divisive Cuccinelli getting the nomination was what gave them the shot they needed to win.
2) Dave Brat unseating Eric Cantor. Cantor was popular in his district, and he was hardly the first candidate to ignore a primary race, or to underestimate the Tea Party's willingness to unseat a popular moderate Republican.
Not only did it unseat one of the Virginia GOP's leaders/favorite sons in favor of a glorified talk radio host, but one of the district's key groups of swing voters - ie, the Jews - never forgot or forgave Bratt for keeping Cantor from becoming the likely first Jewish Speaker of the House. Though the gutting of the VA GOP moderate wing didn't help either. Also, when Virginia's districts got redrawn, a firebreather (and a useless and powerless one at that) like Bratt was never going to keep control of the Virginia 7th District after they cut out a good chunk of his native Hanover County, which is why he lost it to Spanberger. Cantor on the other hand, would be able to hold it.
3) Corey ****ing Stewart. My god. The man has cost more Virginia Republicans their jobs than the end of Reconstruction.
Which is why, along with McDonnell's trial, why the Virginia GOP spent the 2010s in the wilderness. Only reason they're coming out now is the state Democrat's top three figures are either into wearing blackface or being investigated for sexual assault.
So let's say Eric Cantor rather than Paul Ryan is the VP nod in 2012. Whether he carries Virginia for the ticket or not - and I think he would - the effects on the Virginia GOP would be profound.
Cantor is now an even bigger figure in Virginia politics - with McDonnell's fall from grace, the biggest in the state. As such, he works to put his thumb on the scale for Bill Bolling to get the nod in 2013 - perhaps by pointing out to Cuccinelli that there's a Senate race next year he'd be better suited for. Thus, Bill Bolling wins handily the Virginia Governor's race in 2013, and in what turns out to be one of 2014's biggest shockers, Senator Mark Warner is defeated by Ken Cuccinelli, who ran with full state GOP backing and party funding, unlike Gillespie.
The increased profile nationally and locally after 2012 has another effect - the Tea Party groups that fueled Brat's primary challenge in OTL are now very split. Cantor isn't just some shmuck in Congress now, he's the former VP nominee, likely next speaker of the house, got Bolling elected and made good on helping Cuccinelli run for Senate, and there's even talk of a run in 2016. It's narrower than those 30 point leads shown in the polls, but Cantor fends off a primary challenge from Brat, only losing in Brat's native Hanover County. He cruises to re-election alongside the GOP wave of 2014 to nobody's surprise.
No, the BIGGEST shock of 2014 for the Virginia GOP though - with Speaker John Boehner stepping down, the gavel is going to Eric Cantor, making history as the highest-ranking Jewish-American to hold US elected office, something that briefly earns celebration from even the most liberal members of the Jewish Community. As the first Virginian to be Speaker of the House since the 1840s, and the first Virginian elected to a prominent national office since Woodrow Wilson, it also makes Cantor the unquestioned kingmaker within the Virginia GOP.
Outside of statistics, it helps that unlike Ryan, Cantor was a workhouse as a Representative - no sooner is he named the Speaker than he gets to work pushing bill after bill to the Senate, though a great deal of them die when they reach Obama's desk.
Of course, all of that might be put to the test with the 2016 election on the horizon - will Cantor run himself? He's popular, from a key swing state he may have delivered in 2012, and now one of the most prominent Republicans in America. The nomination may be his for the taking, but there are still rumors of several other key Republicans looking to run... hell, there's even chatter that Donald Trump of all people may run.
So, MASSIVE changes in Virginia politics, with some ripples eventually affecting things nationally.