A dispute has erupted between President Obama and Democrats in Congress over a proposal to broaden the exemption from new rules that require health insurance plans to cover contraceptives for women free of charge. The prospect of such a change has infuriated many Democrats in Congress, who fought hard to secure coverage of birth control under the new health care law. Senators voiced their objections on Thursday in a telephone conference call with Pete Rouse, counselor to the president. House members registered their objections on Friday in a call with Valerie Jarrett, another member of the president’s inner circle. House members have sent a letter to Mr. Obama urging him not to widen the exemption.