The impact of removing these voters from the equation not only effects things like the Presidential race, which has dire consequences on many policies effecting the country, but also down ticket races like state legislatures and judges, which also have huge impacts for issues like women's rights and LGBT equality. The removal of Democratic voters, and thereby voters more likely to lean socially moderate or liberal, also has a potentially outcome-altering impact on state ballot initiatives, like anti-gay marriage equality bans on the ballot in many state in 2012.
For example, almost all of the Republican photo ID mandates make it more difficult for students to vote. In Texas, you can vote with a gun license but not a student ID. South Carolina and Tennessee expressly prohibit the use of student IDs, while Wisconsin allows student IDs but has strict qualifications that no university ID in the state currently meets. Suppressing young, progressive voters does more than just changing the outcome of one Presidential election-- it shapes social policy by removing their voices from the process and disenfranchising them for years to come. This would set progress on social issues back decades, from reproductive rights to minority issues to LGBT equality.
We have seen throughout our history how restricting voting rights doesn't strengthen us as a country-- it muffles the voices of the very people who most need to be heard. Voter suppression and disenfranchisement is about fear of progress and change. Silencing swathes of the electorate for political gain may seem like a good idea in the short run, but it stagnates our country. These laws prove some haven't learned from the mistakes and growth of those before us that fought and died for the right to cast that ballot on election day.
Voting can't be taken for granted-- and its impact on us all can't either.