According to an article by Laura Litvan published at Bloomberg Politics Tuesday, Senate majority leader Mitch McConnell is not in favor of tax reform that brings in less overall revenue. That is, any tax cuts would have to be offset by tax increases. A cut in marginal income tax rates, for example, would need to be offset by canceled tax credits or deductions, or else by a new or higher tax on something else, such as perhaps a "border adjustment tax" that would raise the price of imported goods. This puts McConnell at odds with many colleagues and with a large number of House Republicans.
In recent decades Republican tax cuts have let to lower revenues and a bigger deficit. When President Bill Clinton left office the federal government was running a large surplus and paying down the national debt so fast that had it continued, the debt would have been gone entirely in 2010. But two rounds of tax cuts under George W Bush, combined with wars, the passing of Medicare Part D, and other things, led to massive deficits. (In fairness to Bush, he was reportedly hesitant about the second round of tax cuts, but Vice President Dick Cheney persuaded him to go along with the idea.)
By no means all Republicans agree with McConnell. See this previous post from January.