The Senate is unlikely to pass the GOP's latest tax legislation before the midterms, even if the House votes on the measures this month as planned, the top House tax writer said Wednesday.

House Ways and Means Committee Chairman Rep. Kevin Brady, R-Texas, said "the time is short before the election" to approve bills his party has dubbed its second phase of tax reform. Both the contentious confirmation process for Supreme Court nominee Brett Kavanaugh and challenges in getting Democratic support make quick passage difficult in the Senate.

"From a timing standpoint, we're going to put the ball on the field and move it through the House, to the Senate," Brady told CNBC's "Squawk Box." "It's in three bills, so Leader McConnell's been clear; when I see support, 60 votes, we'll move those three bills as we see it."

He said he thinks the Senate will start considering the tax proposals after November's elections. Democrats are favored to take control of the House, while they have much longer odds of flipping the Senate. Brady said the GOP will "fight to hold" congressional majorities "so we have a chance" to push tax legislation.