On 6/7/2017 Rep. Greg Walden (R-OR-2) signed on to HR 38 to bring the total Co-Sponsors to 195.
You ask what are the chances? Well that depends on Paul Ryan for the House Bill and Mitch McConnell in the Senate. They are the "Gatekeepers" of what get to the floor for a up and down vote. At this point I am not happy with either of them, as I feel they are both anti-Trump Republicans. They don't want to help his agenda and want to control the Republican agenda themselves, as they don't look at him as a real Republican. Some people make the mistake in believing all Liberals are Democrats. They are quite a few Republican Liberals in the Congress. So, that being said, I would give the National Reciprocity Bills (HR 38 and S 446) no better than a 50/50 chance of hitting the floor. Rest assure, that if these bills die, they will be back again under new bill numbers in the next session of Congress. It has been stated by President Donald J. Trump (himself a concealed carry permit holder and lifetime member of the NRA) that he will sign this into law as soon as they hit his desk.
Of course we, in the "Monocracy" of Delaware, cannot count on any support from our Congressional Representatives, because they are all Democrats. It is foolish on how we keep putting these Liberal Progressives anti-gunners, in office and expecting a different result. It's Moronic!