Turn about is fair play. Democrats have every right to block this nominee until after the midterm election cycle. Republicans blocked Merrick Garland, Obama's last pick 6 months before the election, so they could campaign on the SCOTUS, and I would expect that Democrats will do the same.
After campaigning on the SCOTUS--Trump picked a nominee in Niel Gorsuch that Hillary Clinton & Barack Obama voted for in 2006. Niel Gorsuch, a G.W. Bush nominee to the Federal 10th district court of appeals. In fact Democrats confirmed Niel Gorsuch, at a time when they could have easily rejected him, as they were the majority in the Senate at that time.
Here are the Democrats that voted for Niel Gorsuch in 2006.
Niel Gorsuch is the only nominee to my memory that stated during confirmation hearings that Roe v Wade is precedent in the Constitution, meaning set it stone.
Gorsuch to Feinstein: Abortion ruling is 'precedent'
The ONLY reason Democrats tried to block Niel Gorsuch this time around is because they were pissed that Republicans blocked Obama's last nominee, Merrick Garland. But even at that, they didn't put up a huge fight because they obviously liked Niel Gorsuch. This new pick Brett Kavanaugh--look for a yuuuuuge fight.
Democrats have a very good chance of taking back the house, and possibly the senate this coming November, and they are just thinking ahead. If they win back the Senate, it will be they that make the confirmations and decide who the SCOTUS will be. So of course they're going to try and block
Brett Kavanaugh, whether they like him or not.
Blue wave coming this November 2018
It's just politics 101