If Dwight D. Eisenhower were alive today, would he still be a Republican?

The consensus opinion is that Dwight D. Eisenhower, based on his policies and proclamations while in office, would not be a Republican today. Democrats and disgruntled Republicans often used Eisenhower as an example of how far the current Republican Party has moved to the right.
For example, Eisenhower was in favor of keeping taxes high in order to achieve a balanced budget and economic stability. He said:

In spite of some things that I have seen in the papers over the past eight or nine months, I personally have never promised a reduction in taxes. Never.

Under his administration, the highest tax rate, on the very wealthy, was ninety percent. Eisenhower said:

We cannot afford to reduce taxes, reduce income, until we have in sight a program of expenditures that shows that the factors of income and of outgo will be balanced. Now that is just to my mind sheer necessity.

All of this would be utter anathema under the current ideology of the Republican Party, which has demonstrated it will cut taxes at all costs, even if it means driving up the federal deficit. Defending taxation as necessary to the health of the nation would be political death to any current Republican candidate.
Eisenhower also instituted a bold and very successful government spending program on infrastructure when he spearheaded the funding of the interstate highway system. He did this because he had been impressed with the German highway system when he was a general during World War II, but also because he felt the federal government should work to keep employment high. Today, such a spending program on infrastructure is not a part of the Republican agenda. The party no longer believes the government should invest in such projects, believing instead this should be the responsibility of the private sector.
In his farewell address, Eisenhower, who had seen the horrors of war first hand, warned about the importance of reining in the military:

In the councils of government, we must guard against the acquisition of unwarranted influence, whether sought or unsought, by the military-industrial complex. The potential for the disastrous rise of misplaced power exists, and will persist.

He advocated for the use of diplomacy, "intellect" and "decent purpose" to solve international conflicts rather than military might. The Republican Party today, in contrast, puts a premium on military power.
The United States has moved so far to the right since Eisenhower's time that Eisenhower would be a liberal candidate even for the Democratic Party today.