The poster of this article is not measuring high on the “reading comprehension” scale. There’s a big difference between “have to swallow tax increases to get the spending cuts we want’ and “screaming and advocating for higher taxes.”
You seem to have a more basic confusion.
Regardless of whether it is "swallow" (ie., cave like a sissy) or "scream for" more taxes, it's totally unacceptable. Therefore, IF Coburn is saying he would go along ("swallow") ANY tax increases, THEN he is a scumbag.
I will, however, wait for verification/clarification of what Tom said/meant.