I'm not sure if anyone else was having this problem or not, but I found a workaround and wanted to share it with others if they are having the same issue.

The steps I'm using to create the error are as follows:

Starting from the main league page
Click on "Commish Tools"
Under "Keeper Management", click on "Assign Auction Keepers Players"
On this page, the left column has the full list of players, and the right column has the keepers for the team "Team 1" (my team). None of the players in the 2nd column have values (they are all blank)
I click in the blank box (under "Cost) in the right column for Arian Foster, and input $58.
If I hit the "enter" key or click into another box (Jimmy Graham for example), I get the "The cost you entered puts the team over its maximum budget." error.
If I click "Ok" on the error, and then try and and click "Save Progress" at the top, then I get the "An error occurred while saving your changes" error.
When I click "Ok" through that error, the right column with the team keepers says "Saving" and keeps spinning as if it's working, but it never finishes.

On the same page, I also tried adding Ray Rice to the #17 roster spot. When I do that, it populates the value as $42, and if I scroll down to the "Budget Overview", it reflects that I've spent $42 of my $200 budget. When I click "Save Progress" at the top however, I still get the "An error occurred while saving your changes" error.

I also get the "An error occurred while saving your changes" error if I try and change the teams with the drop down menu.

The workaround:

When I input a price for Arian Foster, I get the error. When I click through the error, the price stays. I filled out the values for the rest of the players, clicking through the error as needed. After I did that, I went to the bottom and clicked "Save and Exit". I went back into the Assign Auction Keeper Players and it saved the information. I was then able to go to the 2nd team in the drop down list (but not the 3rd). I did the same thing to fill out their values, saved and exit, and went back in. I was now able to go to the 3rd team, with the values saved for the 1st and 2nd. Proceed with the rest of the teams.