Do Arminians believe in a work based salvation?

You will hear this from some Calvinist that Arminians believe in a works based salvation that leads straight back to Romanism. Is the Calvinist right and Arminianism goes against the Reformation principle of Sola Fide?

  

  Now let's define what is a works based salvation I would define it as a system that says the works we do merit eternal life alongside faith. But do the best theologians of Arminianism affirm that John Wesley says  "The righteousness of Christ is the whole and sole foundation of all our hope. It is by faith that the Holy Ghost enables us to build upon this foundation. God gives this faith; in that moment we are accepted of God; and yet, not for the sake of that faith, but of what Christ has done and suffered for us. " Arminius echos the same thing "I believe that sinners are accounted righteous solely by the obedience of Christ; and that the righteousness of Christ is the only meritorious cause on account of which God pardons the sins of believers and reckons them as righteous." So already two of the foundational theologians only believe in one meritorious cause for salvation and that is Christ. But I usually hear from Calvinist that Arminians make faith a work since man's will is not passive. 

The problem here is that Arminians say faith is a gift from God all the human will does is accept the gift or reject this gift. I will give a example to illustrate my point if a rich man gave a poor man money and the poor man receives the gift would you count that as a work? No one would say the poor man worked for that money he just accepted the gift. So in the same way man accepts the gift of faith from God it doesn't make faith a work. Now Calvinist will say that the only way faith can be a gift is if the human will is passive and it does nothing. But as we seen from the example I give accepting a gift is not a work that we can boast about. The Calvinist will have to say my example I gave is a work since the poor man accepted the gift. Since that's the only way to be consistent if you say that the only way something is a gift is if the receiver is purely passive. We also don't say man without grace accept this gift man needs prevenient grace to accept the gift of faith. 

 So to say Arminians believe in works based salvation is wrong since the orthodox view within our tradition has always been Christ is the only meritorious cause for our salvation. So to say we believe in works based salvation is to admit that you never read any good Arminian theologian.