First Amendments rights are NOT ABSOLUTE!!! Yes it is coercing a person to do something that person doesn't want to do. The government does have a right to do so. Cases that involve the first amendment invoke strict scrutiny (the highest level of judicial review) under strict scrutiny the government has to show that it is serving a "compelling governmental interest" and that it is doing so in the "least restrictive way in possible." Mainting the health and general welfare of a nation is a legitimate government interest (such as paying for contraception and blood transfusions.) There is a law school saying "strict in theory, fatal in fact," but this saying is more of a myth and doesn't hold up under empirical observation, 59% of court cases challenging laws involving religious freedom survive strict scrutiny (link below)
http://papers.ssrn.com/sol3/papers.cfm?abstract_id=897360

Furthermore you are dead wrong on the legal issues here Joel. 28 of 50 states already require health care plans in their state cover contraception. Some stats (italics is me quoting the below link, parts in parenthesis but no italics are Roland00 talking to make the comment a little more clear)

HIGHLIGHTS:
* 28 states require insurers that cover prescription drugs to provide coverage of the full range of FDA - approved contraceptive drugs and devices; 17 of these states also require coverage of related outpatient services.
* 2 states exclude emergency contraception from the required coverage.
* 1 state excludes minor dependents from coverage.

* 20 states allow certain employers and insurers to refuse to comply with the mandate. 8 states have no such provision that permits refusal by some employers or insurers. (The States are Colorado, Georgia, Iowa, Montana, New Hampshire, Vermont, Washington, Wisconsin so 8 states that require even churches to fund contraception)
(These remaining numbers are for the 20 states that require contraception but have exceptions. Here are the exceptions)
* 4 states include a “limited” refusal clause that allows only churches and church associations to refuse to provide coverage, and does not permit hospitals or other entities to do so .
* 7 states include a “broader” refusal clause that allows churches, associations of churches, religiously affiliated elementary and secondary schools, and, potentially, some religious charities and universities to refuse, but not hospitals.
* 8 states include an “ expansive ” refusal clause that allows religious organizations , including at least some hospitals , to refuse to provide coverage; 2 of these states also exempt secular organizations with moral or religious objections. (An additional state, Nevada, does not exempt any employers but allows religious insurers to refuse to provide coverage; 2 other states ex empt insurers in addition to employers.)
* 14 of the 20 states with exemptions require employees to be notified when their health plan does not cover contraceptives.
* 4 states attempt to provide access for employees when their employer refuses to offer contraceptive coverage, generally by allowing employees to purchase the coverage on their own, but at the group rate.
http://www.guttmacher.org/statecenter/spibs/spib_ICC.pdf