From his speech in Michigan earlier today:

The President went to Michigan with the obvious purpose of throwing punches in the right-to-work battle. Interesting. Remember when Obama told a senator “I won” when questioned on his stimulus plan? Well, Republicans won in Michigan. Elections have consequences.

More importantly, the President’s argument makes zero sense. He presupposes that with right-to-work comes lower wages, which is categorically false.

From 2000 to 2010, employment in right-to-work states increased 2.3 percent, compared to a 4.0 percent decline in non-right-to-work states. Indiana saw employment decrease 6.9 percent over the same period. That means Indiana lost roughly 207,000 jobs over the past 10 years. In contrast, 1.2 million jobs were created in right-to-work states.

[…]

Between 2000 and 2010, personal income grew 57.5 percent in right-to-work states, compared to 40.5 percent in non-right-to-work states. Indiana saw personal income grow a paltry 35.4 percent over the same period.

The difference remains when you look at disposable personal income (the money you have left to spend after taxes). From 2000 to 2010, disposable personal income increased 65.3 percent in right-to-work states, compared to 49.4 percent in non-right-to-work states. Indiana managed a meager 41.8 percent increase over the same time period.

Then there is the cost of living, which tends to be lower in right-to-work states. A study by the Missouri Economic Research and Information Center found that in 2009, after adjusting for the cost of living, annual per-capita disposable income was $35,543 in right-to-work states, compared to $33,389 in non-right-to-work states. That equates to a $2,154 premium each year for those living in right-to-work states.

Additionally:

 Right-to-work states are much more attractive for businesses investment. Unionized firms earn lower profits, invest less, and create fewer jobs than comparable nonunion firms.

And more:

The main reasons people claim a state should not adopt Right to Work laws are that they lead to lower wages, are damaging to unions, and are morally wrong because they allow people to receive union services without paying for them. This paper’s critical analysis of Right to Work literature has provided strong evidence that the first two potential drawbacks of Right to Work laws are red herrings.  Numerous credible studies have shown that real wages in Right to Work and non-RTW states are about the same, and if anything Right to Work states have slightly higher real wages.  Additionally, although Right to Work laws do make it easier for people to free ride or receive union services without paying for them, the best estimate available suggests the proportion of people who are truly taking advantage of unions in this way is insignificant.  As to how Right to Work laws affect union membership, the jury is still out.  Most research suggests that total union membership within a state could decrease by between zero and eight percent after a state adopts a Right to Work law.  This would be the most significant negative effect to a state of adopting Right to Work laws.  However, it seems fairly safe to say that the possible reduction in union size does not negatively affect workers’ wages.

[…]

When one weighs the benefits of Right to Work laws, mainly stronger economic growth and new job creation, against the negative effects of Right to Work laws, mainly the possibility of somewhat weakened unions, the choice is clear.  In either case the real wages people earn are the same, but the economic growth and job creation are different.  States wanting to be well positioned for success in the 21st century should adopt a Right to Work law.

And still more:

The reason why the Right to Work Floridian is better off than the union-controlled Californian is not, however, the exclusive result of differences in taxes.  Certainly, the lower tax rate makes a difference.  But more important is the option not to join a union and pay union dues.  The dues the Floridian does not have to pay make for money he now has available to use, save, or invest as he chooses.

Additionally (includes figures showing a lower cost of living in RTW states):

The fact is, Right to Work laws safeguard employees’ freedom of association evenhandedly: They prohibit the firing of employees for refusal to join or pay “fees” to a union, and they also prohibit termination for joining or financially supporting a union.

[…]

Where their difficulty lies is in explaining why they believe the law should protect one employee’s right to support a union, but at the same time authorize the firing of another employee who chooses not to support the same union.

The President’s claim that RTW brings with it lowered wages is demonstrably false. It’s the statement of a politician working to save one of his biggest cash cows: union bosses.