Was Ike was the most Responsible Republican President since Lincoln?

He was in my opinion.  He accomplished a number of things, but most astoundingly, when he swept into office in 1953 he brought so many Republicans on his coattails that Republicans had majorities in both houses of Congress for the only time between 1932 and 1995.  That situation only existed for two years, but during that two year session Congress enacted the 1954 Tax Code that had tax rates as high as 90% on the income of really wealthy people.  It solved the huge budget deficit problem that we had developed during the great depression and WW II.

In the two prior sessions of Congress Democrats had a majority and had first enacted many of the taxes on the income of the wealthiest Americans, but I don't think that diminishes Ike's leadership on the issue.  It would have been easy to have cut those high tax rates back to keep wealthy constituents happy as he looked forward to his reelection campaign, but he recognized we needed to deal with the debt and pushed the Republicans in Congress to act responsibly.

He still got reelected (although Republicans lost their majorities in both houses) and he left office with the country in pretty sound financial shape.  Certainly no Republican President since then can say that.