You might be able to soon. The Connecticut legislature is considering a bill that would create a fund, paid for by employee (not employer) contributions, to pay employees when they need to take leave in certain circumstances. This bill would provide full pay after tax for 12 weeks for up to 12 weeks, up to $1000 per week. The payouts would be funded by an additional tax levied on employee paychecks. It would apply to employers with more than two employees, unlike the FMLA, which only applies to employers with more than 50 employees. California, New Jersey, and Rhode Island currently have programs like this.