WASHINGTON — One by one, they queued up in the aisles of the House of Representatives, eager for their one minute to unload on President Obama’s signature legislative achievement.

For many Republicans, this was one of the major reasons for coming to Washington in the first place. And they were not going to miss their chance — whether it was their 37th time voting to repeal the 2010 health care overhaul, or their first.

“Obamacare is enforced by the I.R.S., probably the most feared federal agency in the United States government,” said Representative Michele Bachmann of Minnesota, offering one of the newest and more novel reasons Americans should fear the law. The dreaded Internal Revenue Service, she said, had just been caught targeting people from all walks of life: Christians, friends of Israel, people for less debt and more jobs, to name a few.