House and Senate members from both parties have been obstructing nominees they don't like for decades. This isn't anything new, and it's an important part of the balance of power in the government. They should certainly be able to use their power to block Supreme Court nominees if they don't feel like it's a good fit for the country.
As hyperbolically advertised the power of the president is these days, the truth is that it is difficult for a president to impose his legislative will. People seem to be of the conclusion that legislative accomplishment is the mark of a good presidency, but checks and balances are in place for a reason. It should not be easy for any branch to make changes to our country's core and foundation. That's not to say that the constitution is perfect, but people want to neglect and turn away from the many values and principles that actually made America (at one point, unarguably) the most powerful country in the world. Stop trying to make it so easy to uproot roots just because you can.
Right now Republicans agree. Congressmen should not be able to block a Supreme Court Nominee. They have been blocking a nominee for almost a year and now say that they shouldn't be able to do it. It is the highest form of hypocrisy. The mention of Democratic blocking of a nominee is decried 'Unamerican' but they themselves have done it. Republicans have broken the system by acting in their own party's interest instead of America's interests.
At the very beginning of the Republican primary, all of the other candidates were shocked that Trump wouldn't say he would support the eventual candidate. However, Trump ended up winning the nomination. The Republicans did and continue to do everything they think might work in order to obstruct Trump's agenda. It shouldn't be allowed.