Can mortage company proceed with forclosure if the IRS has a lien on the home

It's a numbers game. If there is enough left over after the IRS is satisfied to make it worthwhile for the lender to go through the process there is no reason why it wouldn't foreclose. I have also seen cases where the IRS has agreed to take less to allow other people to be repaid. They can be negotiated with.

Generally I disagree that the mortgage company has to consider what is due to IRS. Generally the mortgage lien is superior to the IRS lien, and if that is the case, there is no meaningful impediment to the mortgage company proceeding with the sale.

While it is not my objective to turn this into a debate, IRS liens come behind (are subordinate to) purchase money mortgages, even when the IRS lien was on record first. This is enunciated in IRS Revenue Ruling 68-57. And, any IRS liens filed AFTER the recording of a mortgage, whether purchase money or refinance, by definition are subordinate to the mortgage in question. Therefore, foreclosure of a mortgage where an IRS lien is subordinate takes out the IRS lien AS TO THAT PROPERTY. The IRS may have a right of redemption, whereby the IRS would have the right to pay off the mortgage-holder's judgment, however if the property is upside down relative to the mortgage, or even slightly right side up, there is no reason why the IRS would want to do that, and so will normally waive it right of redemption UNLESS THERE IS SIGNIFICANT EQUITY above the total due to the mortgageholder. In the normal case, a mortgage is not originated if there is an existing IRS lien (unless it is a purchase money mortgage covered by RR 68-57) and so therefore there is rarely a situation where the mortgageholder has to worry about the IRS lien being a priority.