Faculty member at a US PhD-granting institution (and advisor of undergrads!) here.

Firstly, you should talk to your undergraduate advisor or mentor, particularly in US history--someone you were close to who might be able to give you honest and useful advice. In lieu of that, I'll tell you the important things straight-up: the job market is terrible and crowded; there are still far more grad applicants (many with big-name mentors from big-name undergrad programs) than places for them; and unless you land a grad spot in a very good program with a well-known advisor, you'll be at a major disadvantage in the end. Be sure it's really what you want to do, and make sure you've got a plan B because it simply doesn't work out for most people. (We've taken to simply not extending offers to strong candidates unless we feel sure that they'll get a job with our PhD and unless we can pay their freight the whole way--but even then, we placed fewer than 50% of our PhD recipients in jobs this year.)

Second: you didn't get to do any research or work with primary sources as an undergraduate? Our capstone practicum requires it--in part to assure that anyone going forward will have evidence of their skill for employers or grad programs. That's a significant liability not to have, because good programs will ask for writing samples (that experience thing). Do you have any major papers that used primary sources to rely upon, or that you can revise to include the same? The assessment and use of primary sources is, after all, such a huge part of what we do that it must be demonstrable. US history has an advantage in that so much material is available (if you're in the USA, that is). In any case, angle your writing sample with the next point in mind.

(Third:) In terms of positioning, you should have an idea of what rough era or subject within US history interests you (ideally this should hew to your writing sample as well). With so many Americanists around, that narrowing is important. But more than that, it lets you identify the key people in your field--the ones who wrote the influential books and articles--so you can track them down as possible advisors. The identification of a possible advisor, and contact with that person, is essential to success. It also cuts down the number of programs you have to dig through. Look at where they are in terms of prestige, who else is working there in US history (you'll have to constitute a committee after all), and where their alumni get jobs. If those all are positive, contact the person and introduce yourself (with a CV?), in a proper letter if possible. If the prospects there don't look promising, you can email asking for advice, and many historians are happy to give it. Some aren't, and some will be dismissive of a letter, but that can tell you something about their attitudes. In any case, you will need an advisor to go to bat for you to get into most programs [and at the other end, to land you a job]. Contacting them, and convincing them that you're serious and capable, is an excellent way to tip that scale. It shows initiative and interest, and makes you a person instead of just a random applicant.

Finally, whatever you do, don't pay (much) for grad school. A good program should have assistantships or fellowships that cover the majority of costs. If you must pay to climb the ladder at the MA level at a weaker school, just to get research and grad-level work into your experience base, do as little of it as possible. The pay when you get out, even landing a job like mine, is not particularly good--and for the growing ranks of adjuncts it's scandalously bad. Someone here might have a good recent piece from the Chronicle or AHA Perspectives on hand to aid the reality check. Have your backup plan ready.

I'm sorry to sound so negative, but it's necessary to be honest about the prospects. If you're determined, you can do things to improve your chances--do the research necessary to make good contacts, master skills on your own or in an intermediate program, and make sure you test well and have a good strong academic track record to show--but be aware that it's a hell of a slog, even if you're lucky enough to have a good academic pedigree.

[edit: as a note to what /u/Timmyc62 said above, I wouldn't say that most top-flight PhD programs require the MA first, but if you can apply with one in hand they will take time off of your program and look at you more seriously. This is what I did in grad school. Here, we actually severed our MA from our PhD deliberately a few years ago, in what used to be a BA-to-PhD program; we can offer the latter, but usually we only offer the former, with the hopes that MA students will either go to an even stronger program or find a perfect fit here, assuming they stay in academia at all. But if you look at the program information on any given website, they should tell you how they approach the MA. If you are determined to go into grad study in history and don't have a strong pedigree, an MA at a somewhat more prestigious school with a strong and helpful advisor is a great intermediate step--but you have to get in there first.]

Most PhD programs require you to do a Master's degree first, though some programs offer a combined degree. My process was as follows: in the penultimate semester of my undergrad degree, I asked one of the profs with whom I had a fairly good relationship (i.e. knew each other, relatively similar research interests) to give me some recommendations on where I could go to further pursue my research focus. She gave me some universities around the country, and also the names of some profs who would probably be interested in supervising my research. I chose one (due to my fairly narrow focus on military conflict studies) and applied to it after sending an email to one of the recommended profs at the prospective program to discuss whether he'd be interested in being my supervisor. Got accepted, and began my Master's program the next academic year. The semester before I finished my Master's thesis, I also applied to several PhD programs and got accepted to two of them; chose one and am now in it!

So my advice for you would be to talk to one of your undergrad profs who taught you a course on American history. Preferably a prof who knows your academic performance so they can write you a reference letter for the application.