My- my state was a leading indicator of what liberals will be trying to do across the country and are trying to do right now. And I fought against against long odds in a deep blue state, but I was a severely conservative Republican governor.
Thus Erick Erickson at redstate.com complained:
What the heck is a severe conservative? The man who likes to fire people should probably fire Miriam-Webster, in addition to whoever came up with his strategy for Minnesota, Missouri, and Colorado.
A severe conservative? It sounds more like a critique of conservatives from the left than that of a conservative himself
And Molly Ball at the Atlantic focused on the adverbial form, explaining:
Mitt Romney's much-hyped task at the Conservative Political Action Conference: convince this exotic tribe that he was one of them. And so, in his 26-minute speech Friday, the word "conservative" appeared 24 times.
But when Romney went off script, with a single adverb, he described conservatism as if it were a disease.
"I was a severely conservative governor," he said of his time as chief executive of Massachusetts.
According to Politico,
“I have never heard anybody say, ‘I’m severely conservative,’” Rush Limbaugh noted on his show.
“That didn’t get a lot of applause,” firebrand Rep. Steve King (R-Iowa) observed with a tight smile.
“Some things are too funny to comment on,” a laughing Newt Gingrich commented as he walked into the conference to give his own speech.
A quick check of severely's collocates validates Molly Ball's reaction. In the Corpus of Contemporary American English, severely precedes a modifier 1213 times, and more than 98% of the time, the following word is something generally regarded as regrettable if not downright bad. The top 100, in descending order of frequency:
disabled, depressed, ill, limited, injured, retarded, impaired, malnourished, obese, overweight, handicapped, autistic, restricted, divided, disruptive, disturbed, underwieght, allergic, wounded, deformed, overcrowded, brain-damaged, limiting, disappointed, underrepresented, understaffed, critical, abnormal, depleted, flawed, troubled, underfunded, polluted, sprained, disadvantaged, asthmatic, cold, compromised, broken, disoriented, negative, repressed, short, underdeveloped, violent, damaging, debilitating, bruised, disordered, dependent, distressed, dyslexic, eroded, inadequate, infected, demented, degraded, deficient, congested, cropped, anorexic, afflicted, downhill, dysfunctional, embarrassed, fractured, fragmented, hurt, malformed, mutilated, nearsighted, painful, premature, repressive, strained, stricken, undulating, weak, acidic, anxious, bleeding, bipolar, biased, alone, crowded, constricted, dangerous, defective, decayed, delinquent, disciplined, deprived, face-lifted, hearing-impaired
A few other examples involve modifiers that are problematic in the context of use, though they might be a good thing in other cases: severely elevated cholesterol levels or extinction rates; severely high blood pressure; severely active uveitis, etc.
5 instances are a sort of joke, involving references to "severely gifted" children.
And 7 involved the sense of severe that means something like "austere" or "restrained": severely classical, severely handsome.
It would be hard to find any other intensifier so reliably associated with qualities that are negatively evaluated.
Update — Since there's been some discussion in the comments about the relationship between the Xs in "severely X" and the Ys in "severe Y", here are the top 100 nominal collocates of severe:
weather, pain, cases, disabilities, depression, problems, damage, drought, storms, case, brain, punishment, form, blow, headaches, symptoms, restrictions, consequences, recession, problem, injuries, asthma, illness, penalties, shortage, health, burns, head, winter, disease, forms, headache, limitations, conditions, thunderstorms, criticism, budget, injury, side, stress, shortages, storm, hearing, sanctions, disability, discrepancy, heart, impact, learning, water, complications, malnutrition, anxiety, reactions, trauma, flooding, food, limits, diarrhea, pressure, cuts, dehydration, stomach, infection, threat, chest, arthritis, penalty, thunderstorm, malaria, beating, behavior, disadvantage, reaction, back, concussion, hardship, impairment, muscle, test, crisis, decline, handicaps, liver, strains, difficulties, lack, allergies, droughts, loss, acne, difficulty, downturn, effects, mood, attack, erosion, memory, price, repression
And of course, the collocates that are positive or neutral generally turn sour in following positions. Thus "severe head" tends to be followed by injuries, trauma, wounds, or pain, not by scarves, nurse, or room; "severe mood" tends to be followed by swings, disturbances, or disorders, not by improvements or music.