>There is a populist opposition to the law because there are many large companies and labor unions (and Congress itself, including the president) that have been exempted from the law... And there are rumors that the president is going to further exempt certain well-connected labor unions from the tax on high-cost health plans.

How are they except? I am legitimately curious.

>There are religious objections the law because it requires private companies run by very religious people to offer abortion and contraception coverage in the health insurance they offer their employees.

It doesn't require health care plans to provide abortion services. States are allowed to offer plans that have abortion services, if there isn't a state law prohibiting it. However the "abortion" portion of the premium is collected separately, put in a separate account and is only allowed to be used for abortion services. Abortion coverage is completely "opt-in."

http://www.hhs.gov/asfr/of/finpollibrary/financialpolicies/s...

(1)(B) ABORTION SERVICES.—

(i) ABORTIONS FOR WHICH PUBLIC FUNDING IS PROHIBITED.—The services described in this clause are abortions for which the expenditure of Federal funds appropriated for the Department of Health and Human Services is not permitted, based on the law as in effect as of the date that is 6 months before the beginning of the plan year involved.

(i) collect from each enrollee in the plan (without regard to the enrollee’s age, sex, or family status) a separate payment for each of the following:

(I) an amount equal to the portion of the premium to be paid directly by the enrollee for coverage under the plan of services other than services described in paragraph (1)(B)(i) (after reduction for credits and cost-sharing reductions described in subparagraph (A)); and

(II) an amount equal to the actuarial value of the coverage of services described in paragraph (1)(B)(i), and

(ii) shall deposit all such separate payments into separate allocation accounts as provided in subparagraph (C). In the case of an enrollee whose premium for coverage under the plan is paid through employee payroll deposit, the separate payments required under this subparagraph shall each be paid by a separate deposit.

(C) SEGREGATION OF FUNDS.—

(i) IN GENERAL.—The issuer of a plan to which subparagraph (A) applies shall establish allocation accounts described in clause (ii) for enrollees receiving amounts described in subparagraph (A).

(ii) ALLOCATION ACCOUNTS.—The issuer of a plan to which subparagraph (A) applies shall deposit—

(I) all payments described in subparagraph (B)(i)(I) into a separate account that consists solely of such payments and that is used exclusively to pay for services other than services described in paragraph (1)(B)(i); and

(II) all payments described in subparagraph (B)(i)(II) into a separate account that consists solely of such payments and that is used exclusively to pay for services described in paragraph (1)(B)(i).

Every single State in the Union has restrictions on insurance plans that cover abortion and some outlaw it completely. Full list can be seen here:

https://www.aclu.org/maps/bans-insurance-coverage-abortion

As far as employer provided insurance, they mostly covered abortion before anyway...