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Other bills that attach strings to such benefits have not fared well. A Senate committee on Monday killed a proposal from Sen. Charles W. Carrico Sr. that would require people applying for unemployment benefits who were fired for misconduct related to drug use to submit to drug testing. Someone who fails or refuses to participate without a good reason would be barred from receiving benefits for six months.

Another proposal from Sen. William M. Stanley Jr., Franklin Republican, that would require 24 hours per week of volunteer service for unemployment-benefit recipients has been carried over multiple times in the Senate Commerce and Labor Committee.

Meanwhile, the committee also advanced another conservative priority Tuesday morning — legislation that would repeal a mandate that girls receive a vaccination to protect against HPV before they enroll in the sixth grade. Virginia in 2007 became the first state in the country to impose such a mandate, though parents can opt their children out for essentially any reason.

“Parents and doctors are best designed to make those decisions,” said the bill’s sponsor, Delegate Kathy J. Byron, Bedford Republican.

A federal advisory committee in 2006 recommended routine vaccination to help prevent HPV, which can cause cervical cancer. At least 20 states have enacted legislation since that time to require the vaccine, or fund or educate the public about it, according to the National Conference of State Legislatures.

It became an issue late last year during the presidential campaign, with Texas Gov. Rick Perry, a Republican, was criticized for enacting a vaccine mandate by executive order in 2007, only to have it overridden by the state legislature. Rep. Michele Bachmann, Minnesota Republican, then took fire from fellow conservatives after she suggested that the vaccine could cause mental retardation.

A similar measure cleared the Virginia House of Delegates last year but languished in a Senate committee, then stacked with Democrats, that Republicans now control. Delegate Robert G. Marshall, Prince William Republican, has also introduced a measure to repeal the vaccine mandate and, failing that, another that would make the state liable for any injury that results from administering the vaccine.