Edit in JSFiddle

<form action="#" class="ws-validate">
    <div class="form-row">
        <label for="date">only weekdays</label>
        <input type="date" class="disable-weekends hide-spinbtns" data-date-start-view="2" required="" id="date" />
    </div>
    <div class="form-row">
        <input type="submit" />
    </div>
</form>
<p><a href="http://afarkas.github.io/webshim/demos/demos/cfgs/input-date.html" target="_blank">date configurator</a>
</p>
<p><a href="http://afarkas.github.io/webshim/demos/demos/forms.html#Custom-validity" target="_blank">about: addValidators option</a>
</p>

webshim.setOptions('forms', {
    lazyCustomMessages: true,
    addValidators: true
});

webshim.setOptions('forms-ext', {
    replaceUI: 'auto',
    types: 'date'
});

//start polyfilling
webshim.polyfill('forms forms-ext');

$(function () {
    //valuevalidation was renamed to "validatevalue"
    $('input.disable-weekends').on('validatevalue', function (e, data) {
        //check wether data.valueAsDate is provided
        if (data.valueAsDate) {
            var day = data.valueAsDate.getDay();
            return !day || day == 6 ?
                "Please enter only weekdays. {%value} is a weekend." : false;
        }
    });

});

div.ws-invalid input {
    border-color: #c88;
}
.ws-invalid label {
    color: #933;
}
div.ws-success input {
    border-color: #8c8;
}
form {
    margin: 10px auto;
    max-width: 400px;
    min-width: 220px;
}
.form-row {
    padding: 5px 10px;
    margin: 5px 0;
}
label {
    display: block;
    margin: 3px 0;
}
.form-row input {
    width: 220px;
    padding: 3px 1px;
    border: 1px solid #ccc;
    box-shadow: none;
}