Election day should not be made into a national holiday, not because Republicans want to encourage voter suppression, but rather because they believe there are larger issues. Turning Election Day into a national holiday would supposedly help to increase voter turnout. But Republicans don’t believe voter turnout is the issue that the government should be working to solve.
Republicans want to solve the issue of voter fraud, and turning election day into a national holiday won't solve that problem. According to a survey that asked people what they think the biggest problem related to voting was, there was a large split. 72% of Republicans polled saying voting illegally is a larger problem, while 71% of Democrats polled said the same thing about voter suppression.
Election day does not need to be a national holiday because people are worried about the issue of voter fraud. Voter fraud is not something that can be solved by turning election day into a federal holiday.